Details

analyze1.8s (15.4%)

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)

sample3.6s (30.7%)

Results

1.7s	3558×	body	1024	valid
1.0s	1242×	body	2048	valid
508.0ms	1426×	body	512	valid
195.0ms	1399×	body	128	valid
147.0ms	628×	body	256	valid
4.0ms	3×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess19.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

76×	`fma-def_binary64`
57×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
24×	`sub-neg_binary64`
18×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	17	22
2	25	22
3	38	22
4	53	22
5	81	22
6	141	22
7	200	22
8	282	22
9	353	22
10	405	22
11	409	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Stop Event

1×

saturated

Counts

1 → 1

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

36.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	4.0b	(tan.f64 (+.f64 x eps))

series65.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))	eps	-inf
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))	eps	inf
7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))	x	-inf
6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))	x	inf
6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))	eps	0

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

883×	`prod-diff_binary64`
345×	`fma-def_binary64`
172×	`fma-neg_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	169	17
2	2566	17

Stop Event

1×	node limit

Counts

2 → 117

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

909×	`times-frac_binary64`
730×	`fma-def_binary64`
605×	`associate-/l*_binary64`
328×	`associate-/r*_binary64`
192×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1638
1	374	1636
2	1449	1545

Stop Event

1×	node limit

Counts

165 → 147

prune132.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Error

0.1b

Counts

148 → 9

Alt Table

Status	Error	Program
	21.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	32.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.5b	(+.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (cos.f64 x))) (sin.f64 x) (*.f64 (/.f64 1 (cos.f64 x)) (sin.f64 x))))
	33.1b	(+.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)))))))))
	33.2b	(+.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.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)))))
	21.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	21.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	21.3b	(/.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)))
	33.2b	(+.f64 (+.f64 eps (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (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 (cos.f64 x) 2)) (pow.f64 eps 3)) (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)))))

Compiler

Compiled 4163 to 1724 computations (58.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (-.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))
✓	2.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))

series263.0ms (2.3%)

Counts

4 → 96

Calls

24 calls:

28.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))	eps	-inf
28.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))	eps	inf
28.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))	x	inf
28.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))	x	-inf
20.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))	x	-inf

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

332×	`fma-def_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
186×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	59
1	266	56
2	3689	52

Stop Event

1×	node limit

Counts

4 → 132

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
567×	`associate-l_binary64`
483×	`associate-/r*_binary64`
196×	`associate-/r/_binary64`
174×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3402
1	533	3386
2	1890	3309

Stop Event

1×	node limit

Counts

228 → 195

prune220.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	188	7	195
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	192	12	204

Error

0.1b

Counts

204 → 12

Alt Table

Status	Error	Program
	21.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	33.1b	(+.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)))))))))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	33.2b	(+.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.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)))))
	23.5b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 3)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	33.2b	(+.f64 (+.f64 eps (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (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 (cos.f64 x) 2)) (pow.f64 eps 3)) (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)))))
	21.2b	(+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (-.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x))))
	21.2b	(-.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)))
	32.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	21.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	30.0b	(fma.f64 (expm1.f64 (log1p.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	21.3b	(/.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)))

Compiler

Compiled 6265 to 2648 computations (57.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.4b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	2.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))

series483.0ms (4.1%)

Counts

2 → 48

Calls

12 calls:

110.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	eps	inf
100.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	x	inf
99.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	eps	-inf
97.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	x	-inf
13.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)	x	inf

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

300×	`log1p-udef_binary64`
183×	`add-sqr-sqrt_binary64`
172×	`add-cbrt-cube_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	371	60
2	4923	60

Stop Event

1×	node limit

Counts

2 → 63

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
307×	`associate-/r/_binary64`
296×	`unswap-sqr_binary64`
280×	`associate-/l/_binary64`
236×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	7148
1	503	7046
2	2532	6245

Stop Event

1×	node limit

Counts

111 → 98

prune476.0ms (4.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	255	4	259
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	258	13	271

Error

0.1b

Counts

271 → 13

Alt Table

Status	Error	Program
	21.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	33.1b	(+.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)))))))))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	33.2b	(+.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.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)))))
	23.5b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 3)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	33.2b	(+.f64 (+.f64 eps (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (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 (cos.f64 x) 2)) (pow.f64 eps 3)) (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)))))
	42.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) 3) (pow.f64 (sqrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	21.2b	(-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 2)) (/.f64 (pow.f64 (sin.f64 eps) 2) (.f64 (pow.f64 (cos.f64 x) 3) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))))) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))) (pow.f64 (cos.f64 x) 2))) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
	21.2b	(+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (-.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x))))
	32.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	21.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	21.5b	(fma.f64 (fma.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	21.3b	(/.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)))

Compiler

Compiled 12995 to 5650 computations (56.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3))
✓	0.4b	(pow.f64 (tan.f64 eps) 3)
✓	0.4b	(pow.f64 (tan.f64 x) 3)
✓	2.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))

series491.0ms (4.2%)

Counts

4 → 72

Calls

18 calls:

103.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	x	-inf
95.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	x	inf
94.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	eps	inf
93.0ms	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))	eps	-inf
14.0ms	(*.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3))	eps	inf

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

200×	`add-sqr-sqrt_binary64`
189×	`log1p-expm1-u_binary64`
189×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
183×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	74
1	413	72

Stop Event

1×	node limit

Counts

4 → 92

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Rules

952×	`fma-def_binary64`
303×	`unswap-sqr_binary64`
280×	`associate-/l/_binary64`
254×	`times-frac_binary64`
174×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	7484
1	549	7380
2	2707	6267

Stop Event

1×	node limit

Counts

164 → 142

prune238.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	143	12	155

Error

0.1b

Counts

155 → 12

Alt Table

Status	Error	Program
	21.3b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	33.1b	(+.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)))))))))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	33.2b	(+.f64 (fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.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)))))
	28.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (tan.f64 eps) 3))) 1)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	23.5b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 3)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	33.2b	(+.f64 (+.f64 eps (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (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 (cos.f64 x) 2)) (pow.f64 eps 3)) (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)))))
	21.2b	(-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 2)) (/.f64 (pow.f64 (sin.f64 eps) 2) (.f64 (pow.f64 (cos.f64 x) 3) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 2))) (/.f64 (pow.f64 (sin.f64 x) 2) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))) (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))))) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))) (pow.f64 (cos.f64 x) 2))) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1 (*.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
	21.2b	(+.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (-.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 1 (.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)) (sin.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x))))
	32.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.5b	(fma.f64 (fma.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	21.3b	(/.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)))

Compiler

Compiled 7196 to 3397 computations (52.8% saved)

regimes2.7s (22.8%)

Accuracy

Total 0.6b remaining (83.8%)

Threshold costs 0.6b (83.8%)

Counts

267 → 3

Compiler

Compiled 22943 to 13789 computations (39.9% saved)

bsearch109.0ms (0.9%)

Algorithm

2×	binary-search

Calls

2 calls:

47.0ms	eps
45.0ms	eps

Steps

Iters	Point		Range
1.8570140171349828e-29	∈ [	1.6017572821693184e-34	,	1.8777516274324039e-29	]
-0.00022303564752948558	∈ [	-6.915137302554308	,	-8.597776441403568e-5	]

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
13×	`+-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	267
1	97	267
2	112	267
3	127	267
4	136	267
5	141	267
6	143	267

Stop Event

1×

saturated

end511.0ms (4.4%)

Stop Event

1×

fuel

Compiler

Compiled 991 to 586 computations (40.9% saved)

Iter	Nodes	Cost
0	11	22
1	17	22
2	25	22
3	38	22
4	53	22
5	81	22
6	141	22
7	200	22
8	282	22
9	353	22
10	405	22
11	409	22
0	2	2

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Iter	Nodes	Cost
0	11	22
1	17	22
2	25	22
3	38	22
4	53	22
5	81	22
6	141	22
7	200	22
8	282	22
9	353	22
10	405	22
11	409	22
0	2	2

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11

Details

analyze1.8s (15.4%)

sample3.6s (30.7%)

preprocess19.0ms (0.2%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series65.0ms (0.6%)

rewrite53.0ms (0.5%)

simplify38.0ms (0.3%)

prune132.0ms (1.1%)

localize10.0ms (0.1%)

series263.0ms (2.3%)

rewrite57.0ms (0.5%)

simplify67.0ms (0.6%)

prune220.0ms (1.9%)

localize16.0ms (0.1%)

series483.0ms (4.1%)

rewrite61.0ms (0.5%)

simplify126.0ms (1.1%)

prune476.0ms (4.1%)

localize20.0ms (0.2%)

series491.0ms (4.2%)

rewrite37.0ms (0.3%)

simplify111.0ms (1%)

prune238.0ms (2%)

regimes2.7s (22.8%)

bsearch109.0ms (0.9%)

simplify9.0ms (0.1%)

end511.0ms (4.4%)

Profiling

Iter	Nodes	Cost
0	11	22
1	17	22
2	25	22
3	38	22
4	53	22
5	81	22
6	141	22
7	200	22
8	282	22
9	353	22
10	405	22
11	409	22
0	2	2

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	31	11
5	48	11
6	86	11
7	124	11
8	172	11
9	208	11
10	234	11
11	236	11