Details

analyze1.2s (11.2%)

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
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.9s (35.6%)

Results

2.1s	3706×	body	1024	valid
963.0ms	1223×	body	2048	valid
519.0ms	1408×	body	512	valid
174.0ms	1349×	body	128	valid
162.0ms	568×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

36.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.0b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.7b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	2.8b	(tan.f64 (+.f64 x eps))

series77.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
29.0ms	(tan.f64 (+.f64 x eps))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 43

Calls

2 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
909×	`times-frac_binary64`
194×	`associate-+r+_binary64`
142×	`unswap-sqr_binary64`
125×	`+-commutative_binary64`

Counts

91 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2570
1	507	2289
2	1787	2148
3	4965	2145
4	4986	2145
5	4943	2145

prune101.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Error

0.1b

Counts

94 → 7

Alt Table

Status	Error	Program
	22.9b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.5b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
▶	22.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	32.5b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	32.5b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (.f64 5/3 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (.f64 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (.f64 1/3 (pow.f64 eps 3)))))))))))
	22.9b	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
	32.3b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 3139 to 1347 computations (57.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	3.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series323.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

222.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
36.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
34.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
31.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
67×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
57×	`prod-diff_binary64`
49×	`times-frac_binary64`

Counts

4 → 153

Calls

4 calls:

11.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
3.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify275.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

223×	`unswap-sqr_binary64`
200×	`distribute-rgt-in_binary64`
194×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`
185×	`associate-l_binary64`

Counts

249 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	9237
1	852	7571
2	2862	7052
3	4563	7052
4	4990	7052
5	4990	7052
6	4882	7052

prune257.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	8	232
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	226	13	239

Error

0.1b

Counts

239 → 13

Alt Table

Status	Error	Program
	23.1b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))) (cbrt.f64 (tan.f64 x))))
▶	22.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	23.8b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	32.5b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	25.0b	(-.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	22.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))
	32.5b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (.f64 5/3 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (.f64 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (.f64 1/3 (pow.f64 eps 3)))))))))))
	44.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
	22.9b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.5b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	23.7b	(-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	22.8b	(+.f64 (-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x)) 0)
	32.3b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 9115 to 3162 computations (65.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.1b	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	3.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

series275.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

232.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
43.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`*-un-lft-identity_binary64`
113×	`times-frac_binary64`
106×	`add-sqr-sqrt_binary64`
101×	`add-cube-cbrt_binary64`
99×	`prod-diff_binary64`

Counts

2 → 168

Calls

2 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
3.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

simplify183.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-/r*_binary64`
256×	`associate-/r/_binary64`
185×	`unswap-sqr_binary64`
171×	`associate-r_binary64`
146×	`cancel-sign-sub-inv_binary64`

Counts

216 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	352	11480
1	737	8433
2	2598	7644
3	5486	7644

prune311.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	262	13	275

Error

0.1b

Counts

275 → 13

Alt Table

Status	Error	Program
	23.8b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	32.5b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
▶	22.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))
	32.5b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (.f64 5/3 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (.f64 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (.f64 1/3 (pow.f64 eps 3)))))))))))
	22.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (*.f64 (E.f64) (pow.f64 (exp.f64 (tan.f64 x)) (neg.f64 (tan.f64 eps)))))) (tan.f64 x))
	29.1b	(log.f64 (exp.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))))
	44.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
	22.9b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.5b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	43.2b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 1) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	32.3b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	23.9b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x))) 0)
	23.7b	(-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

Compiler

Compiled 11269 to 4182 computations (62.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.1b	(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
✓	0.2b	(*.f64 (sin.f64 x) (tan.f64 eps))
✓	3.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))

series276.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

219.0ms

(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))

35.0ms

(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))

22.0ms

(*.f64 (sin.f64 x) (tan.f64 eps))

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`*-un-lft-identity_binary64`
137×	`add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
90×	`prod-diff_binary64`
82×	`add-cube-cbrt_binary64`

Counts

3 → 185

Calls

3 calls:

16.0ms

(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))

5.0ms

(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))

4.0ms

(*.f64 (sin.f64 x) (tan.f64 eps))

simplify246.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
189×	`associate-/l*_binary64`
173×	`unswap-sqr_binary64`
165×	`associate-r_binary64`
156×	`associate-l_binary64`

Counts

257 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	387	12527
1	888	9744
2	3072	8915
3	4893	8915
4	4921	8915

prune264.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	265	1	266
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	266	13	279

Error

0.1b

Counts

279 → 13

Alt Table

Status	Error	Program
	23.8b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	32.5b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
✓	22.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))
	32.5b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (.f64 5/3 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (.f64 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (.f64 1/3 (pow.f64 eps 3)))))))))))
	22.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (*.f64 (E.f64) (pow.f64 (exp.f64 (tan.f64 x)) (neg.f64 (tan.f64 eps)))))) (tan.f64 x))
	29.1b	(log.f64 (exp.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))))
	44.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
	32.5b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	43.2b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 1) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	32.3b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	23.9b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x))) 0)
	23.7b	(-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	22.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (tan.f64 eps))) (cos.f64 x)))) (tan.f64 x))

Compiler

Compiled 11184 to 3280 computations (70.7% saved)

regimes2.4s (22.2%)

Accuracy

Total 0.2b remaining (56.7%)

Threshold costs 0.2b (56.7%)

Counts

289 → 3

Compiler

Compiled 25473 to 14249 computations (44.1% saved)

bsearch109.0ms (1%)

Steps

Iters	Range		Point
10	2.3898628593282043e-14	0.0016294858784189127	0.0002116841733599596
9	-604.6386325693618	-0.00011386633417659882	-0.00021473042784006286

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
18×	`+-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	257
1	114	257
2	128	257
3	136	257
4	141	257
5	142	257
6	141	257

end376.0ms (3.4%)

Compiler: Compiled 913 to 525 computations (42.5% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze1.2s (11.2%)

sample3.9s (35.6%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series77.0ms (0.7%)

rewrite11.0ms (0.1%)

simplify111.0ms (1%)

prune101.0ms (0.9%)

localize9.0ms (0.1%)

series323.0ms (2.9%)

rewrite38.0ms (0.3%)

simplify275.0ms (2.5%)

prune257.0ms (2.3%)

localize12.0ms (0.1%)

series275.0ms (2.5%)

rewrite51.0ms (0.5%)

simplify183.0ms (1.7%)

prune311.0ms (2.8%)

localize13.0ms (0.1%)

series276.0ms (2.5%)

rewrite55.0ms (0.5%)

simplify246.0ms (2.2%)

prune264.0ms (2.4%)

regimes2.4s (22.2%)

bsearch109.0ms (1%)

simplify11.0ms (0.1%)

end376.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11