Details

analyze1.3s (10.1%)

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 (30.9%)

Results

1.8s	3645×	body	1024	valid
1.2s	1254×	body	2048	valid
495.0ms	1361×	body	512	valid
175.0ms	1367×	body	128	valid
145.0ms	627×	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

36.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.2b	(-.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
✓	1.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.8b	(tan.f64 (+.f64 x eps))

series75.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

46.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
29.0ms	(tan.f64 (+.f64 x eps))

rewrite12.0ms (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))

simplify118.0ms (0.9%)

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

prune96.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Error

0.2b

Counts

94 → 6

Alt Table

Status	Error	Program
	20.9b	(/.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	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
▶	20.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	33.0b	(+.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)))))
	32.8b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	20.8b	(/.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)))))

Compiler

Compiled 2985 to 1249 computations (58.2% saved)

localize10.0ms (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 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	1.8b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series416.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

227.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
122.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
37.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
28.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite117.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64`
74×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

4 → 171

Calls

4 calls:

85.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
6.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify241.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

228×	`unswap-sqr_binary64`
225×	`associate-+r+_binary64`
225×	`distribute-rgt-in_binary64`
203×	`distribute-lft-in_binary64`
184×	`associate-l_binary64`

Counts

267 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	10657
1	925	9025
2	3170	8501
3	4767	8501
4	4923	8501

prune306.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	235	10	245
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	239	12	251

Error

0.1b

Counts

251 → 12

Alt Table

Status	Error	Program
	32.8b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	20.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	20.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
▶	20.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 eps) (tan.f64 x)))) (tan.f64 x))
	21.0b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	41.8b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.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)))))
	21.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	20.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 x))) (/.f64 (sin.f64 eps) (.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x)))
	21.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	33.0b	(+.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)))))
	32.8b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	25.7b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 9865 to 3429 computations (65.2% saved)

localize10.0ms (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 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 eps) (tan.f64 x))))
✓	0.2b	(*.f64 (tan.f64 eps) (tan.f64 x))
✓	1.8b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 eps) (tan.f64 x)))) (tan.f64 x))

series396.0ms (3.2%)

Counts

3 → 72

Calls

3 calls:

241.0ms

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

120.0ms

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

35.0ms

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

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`*-un-lft-identity_binary64`
72×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

3 → 153

Calls

3 calls:

13.0ms

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

6.0ms

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

4.0ms

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

simplify271.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

211×	`distribute-rgt-in_binary64`
209×	`associate-+r+_binary64`
203×	`unswap-sqr_binary64`
196×	`distribute-lft-in_binary64`
183×	`associate-r_binary64`

Counts

225 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	10014
1	875	8405
2	3037	7881
3	4707	7881
4	4986	7881
5	4922	7881

prune304.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	278	12	290

Error

0.1b

Counts

290 → 12

Alt Table

Status	Error	Program
	32.8b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	20.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
▶	20.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
✓	20.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 eps) (tan.f64 x)))) (tan.f64 x))
	21.0b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	41.8b	(+.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.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)))))
	21.5b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	20.9b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 x))) (/.f64 (sin.f64 eps) (.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x)))
	21.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	33.0b	(+.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)))))
	32.8b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	25.7b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 10707 to 3684 computations (65.6% saved)

localize11.0ms (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 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	1.8b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

series409.0ms (3.3%)

Counts

2 → 48

Calls

2 calls:

230.0ms

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

179.0ms

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

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`tan-quot_binary64`
15×	`associate-r_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 75

Calls

2 calls:

11.0ms

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

10.0ms

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

simplify157.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
219×	`associate-l_binary64`
211×	`cancel-sign-sub-inv_binary64`
203×	`unswap-sqr_binary64`
190×	`associate-+r+_binary64`

Counts

123 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	5334
1	804	5228
2	2882	5123
3	4934	5123

prune352.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	220	5	225
Fresh	4	6	10
Picked	1	0	1
Done	1	0	1
Total	226	11	237

Error

0.1b

Counts

237 → 11

Alt Table

Status	Error	Program
	32.8b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	20.9b	(/.f64 (.f64 (cos.f64 x) (-.f64 (/.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 eps) (sin.f64 x)))) (*.f64 (cos.f64 eps) (pow.f64 (cos.f64 x) 2)))
	20.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	21.6b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cos.f64 x)) (.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (sin.f64 x))) (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)))
	20.9b	(/.f64 (.f64 (cos.f64 x) (-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (cos.f64 eps) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))) (.f64 (pow.f64 (cos.f64 x) 2) (.f64 (cos.f64 eps) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))
	20.8b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps)))))) (tan.f64 x))
	33.0b	(+.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)))))
	20.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))) (tan.f64 x))
	32.8b	(+.f64 (/.f64 (.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (.f64 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	25.7b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	21.0b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))

Compiler

Compiled 7836 to 3100 computations (60.4% saved)

regimes3.5s (28.3%)

Accuracy

Total 0.4b remaining (78.5%)

Threshold costs 0.4b (78.5%)

Counts

352 → 3

Compiler

Compiled 31986 to 17141 computations (46.4% saved)

bsearch108.0ms (0.9%)

Steps

Iters	Range		Point
8	1.0952304137482734e-23	2.7041605076058555e-20	2.6741431082075642e-20
9	-14.363777818310458	-6.046066070134805e-7	-2.9674248494807262e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
14×	`*-commutative_binary64`
12×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	178
1	75	178
2	90	178
3	111	178
4	124	178
5	132	178
6	135	178
7	134	178

end352.0ms (2.8%)

Compiler: Compiled 760 to 439 computations (42.2% 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

analyze1.3s (10.1%)

sample3.9s (30.9%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series75.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify118.0ms (0.9%)

prune96.0ms (0.8%)

localize10.0ms (0.1%)

series416.0ms (3.3%)

rewrite117.0ms (0.9%)

simplify241.0ms (1.9%)

prune306.0ms (2.4%)

localize10.0ms (0.1%)

series396.0ms (3.2%)

rewrite41.0ms (0.3%)

simplify271.0ms (2.2%)

prune304.0ms (2.4%)

localize11.0ms (0.1%)

series409.0ms (3.3%)

rewrite29.0ms (0.2%)

simplify157.0ms (1.2%)

prune352.0ms (2.8%)

regimes3.5s (28.3%)

bsearch108.0ms (0.9%)

simplify8.0ms (0.1%)

end352.0ms (2.8%)

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