Details

analyze741.0ms (7.8%)

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 (18.9%)

Results

789.0ms	2085×	body	1024	valid
502.0ms	4661×	body	128	valid
293.0ms	1017×	body	512	valid
97.0ms	485×	body	256	valid
4.0ms	8×	body	2048	valid

Compiler

Compiled 50 to 26 computations (48% saved)

simplify91.0ms (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
	0.3b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
▶	0.3b	(/.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)

localize8.0ms (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))

series95.0ms (1%)

Counts

4 → 48

Calls

4 calls:

63.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
14.0ms	(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))

rewrite80.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

872×	`log1p-expm1-u_binary64`
872×	`expm1-log1p-u_binary64`
248×	`prod-diff_binary64`
145×	`egg-rr`
89×	`add-sqr-sqrt_binary64`

Counts

4 → 145

Calls

4 calls:

75.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
75.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
75.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
75.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	44
1	176	44
2	2192	44
3	5841	44
0	0	0
1	0	0

simplify104.0ms (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

193 → 178

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

prune361.0ms (3.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	163	15	178
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	15	180

Error

0.0b

Counts

180 → 15

Alt Table

Status	Error	Program
	0.4b	(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))) -1)
	0.7b	(+.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) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) 1 (*.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1)))
▶	0.3b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (tan.f64 x) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (tan.f64 x) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (tan.f64 x) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (tan.f64 x) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) 3) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)
	0.8b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (tan.f64 x) 2)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	4.2b	(/.f64 (log1p.f64 (expm1.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.3b	(/.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))))

Compiler

Compiled 6817 to 3947 computations (42.1% saved)

localize12.0ms (0.1%)

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))
✓	0.2b	(/.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)))
✓	0.2b	(*.f64 (sin.f64 x) (tan.f64 x))

series108.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

68.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
16.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))
15.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
8.0ms	(*.f64 (sin.f64 x) (tan.f64 x))

rewrite98.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

594×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
173×	`egg-rr`
121×	`add-sqr-sqrt_binary64`

Counts

4 → 173

Calls

4 calls:

91.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
91.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))
91.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
91.0ms	(*.f64 (sin.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	237	43
2	3185	43
3	5091	43
0	0	0
1	0	0

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
782×	`times-frac_binary64`
342×	`cancel-sign-sub-inv_binary64`
251×	`div-sub_binary64`
247×	`sub-neg_binary64`

Counts

221 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	835
1	151	835
2	371	831
3	1091	829
4	3118	829
5	4684	829
6	4881	829
7	5050	829

prune407.0ms (4.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	199	4	203
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Error

0.0b

Counts

218 → 12

Alt Table

Status	Error	Program
	0.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) 1 (*.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1)))
	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 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.8b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	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 (pow.f64 (tan.f64 x) 2) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 1 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))))
	0.4b	(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))) -1)
	0.8b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (tan.f64 x) 2)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
▶	0.4b	(/.f64 (-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) 3) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)
	0.4b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (/.f64 1 (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (/.f64 1 (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) 1) (.f64 (/.f64 (/.f64 1 (cos.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) 1))))

Compiler

Compiled 8260 to 4597 computations (44.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series112.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

67.0ms	(/.f64 (-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
16.0ms	(.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))
16.0ms	(-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x)))))
12.0ms	(*.f64 (tan.f64 x) (/.f64 1 (cos.f64 x)))

rewrite104.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

855×	`prod-diff_binary64`
177×	`egg-rr`
133×	`add-sqr-sqrt_binary64`
123×	`log1p-expm1-u_binary64`
123×	`expm1-log1p-u_binary64`

Counts

4 → 177

Calls

4 calls:

97.0ms	(/.f64 (-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
97.0ms	(.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))
97.0ms	(-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x)))))
97.0ms	(*.f64 (tan.f64 x) (/.f64 1 (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	64
1	263	43
2	3336	43
3	5021	43
0	0	0
1	0	0

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
536×	`cancel-sign-sub-inv_binary64`
418×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`
272×	`sub-neg_binary64`

Counts

225 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	823
1	164	823
2	411	819
3	1232	819
4	2869	819
5	4735	819
6	4896	819
7	5025	819

prune390.0ms (4.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	206	13	219

Error

0.0b

Counts

219 → 13

Alt Table

Status	Error	Program
	0.4b	(/.f64 (/.f64 (neg.f64 (-.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 3))) (neg.f64 (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (pow.f64 (tan.f64 x) 2) 2))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) 1 (*.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 1)))
	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 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.4b	(pow.f64 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (pow.f64 (tan.f64 x) 2))) -1)
	0.4b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (/.f64 (tan.f64 x) (cos.f64 x)) 1)))) (fma.f64 (neg.f64 (/.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (/.f64 (tan.f64 x) (cos.f64 x)) 1) (.f64 (/.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (/.f64 (tan.f64 x) (cos.f64 x)) 1))))
	0.4b	(+.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))))
	0.8b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (tan.f64 x) 2)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.4b	(/.f64 (-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.8b	(/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) 3) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
▶	0.4b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)

Compiler

Compiled 9329 to 5105 computations (45.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
✓	0.3b	(pow.f64 (tan.f64 x) 2)
✓	0.3b	(log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
✓	0.3b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)

series2.2s (23.1%)

Counts

4 → 48

Calls

4 calls:

1.1s	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)
1.1s	(log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
11.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
9.0ms	(pow.f64 (tan.f64 x) 2)

rewrite152.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`prod-diff_binary64`
423×	`fma-udef_binary64`
270×	`fma-def_binary64`
218×	`egg-rr`
214×	`fma-neg_binary64`

Counts

4 → 218

Calls

4 calls:

146.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
146.0ms	(pow.f64 (tan.f64 x) 2)
146.0ms	(log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
146.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	57
1	243	57
2	2895	57
3	4830	57
4	4899	57
5	4906	57
0	0	0
1	0	0

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
532×	`cancel-sign-sub-inv_binary64`
434×	`sub-neg_binary64`
281×	`fma-neg_binary64`
233×	`times-frac_binary64`

Counts

266 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	1372
1	158	1348
2	416	1344
3	1288	1342
4	4295	1342
5	4954	1342
6	4998	1342
7	4956	1342

prune543.0ms (5.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	247	5	252
Fresh	6	5	11
Picked	1	0	1
Done	0	1	1
Total	254	11	265

Error

0.0b

Counts

265 → 11

Alt Table

Status	Error	Program
	0.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) 3)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2)))) (cbrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))))) (cbrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2)))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))
	0.4b	(/.f64 (/.f64 (neg.f64 (-.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 3))) (neg.f64 (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (pow.f64 (tan.f64 x) 2) 2))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	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 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (/.f64 1 (cos.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.4b	(/.f64 (-.f64 1 (-.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(+.f64 (+.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (neg.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2))) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2))))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2))) 2)) (.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2))) 2)))))
	0.4b	(+.f64 (+.f64 1 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))) -1)
	0.8b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (tan.f64 x) 2)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.4b	(/.f64 (-.f64 1 (.f64 (sin.f64 x) (.f64 (tan.f64 x) (/.f64 1 (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (*.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) (pow.f64 (tan.f64 x) 4)))))
	0.4b	(+.f64 (+.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (neg.f64 (.f64 (/.f64 (tan.f64 x) (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (tan.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (+.f64 1 (pow.f64 (tan.f64 x) 2)))) (/.f64 (tan.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (tan.f64 x) 1))))

Compiler

Compiled 8409 to 5919 computations (29.6% saved)

regimes1.5s (15.7%)

Accuracy

Total 0.2b remaining (74.6%)

Threshold costs 0.2b (74.6%)

Counts

306 → 1

Compiler

Compiled 37086 to 24806 computations (33.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	15	25
2	19	25
3	21	25
4	22	25
5	21	25

end268.0ms (2.8%)

Compiler: Compiled 485 to 328 computations (32.4% saved)

Details

analyze741.0ms (7.8%)

sample1.8s (18.9%)

simplify91.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series95.0ms (1%)

rewrite80.0ms (0.8%)

simplify104.0ms (1.1%)

prune361.0ms (3.8%)

localize12.0ms (0.1%)

series108.0ms (1.1%)

rewrite98.0ms (1%)

simplify94.0ms (1%)

prune407.0ms (4.3%)

localize13.0ms (0.1%)

series112.0ms (1.2%)

rewrite104.0ms (1.1%)

simplify99.0ms (1%)

prune390.0ms (4.1%)

localize11.0ms (0.1%)

series2.2s (23.1%)

rewrite152.0ms (1.6%)

simplify108.0ms (1.1%)

prune543.0ms (5.7%)

regimes1.5s (15.7%)

simplify2.0ms (0%)

end268.0ms (2.8%)

Profiling