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)

sample3.6s (32.8%)

Results

1.7s	3629×	body	1024	valid
984.0ms	1259×	body	2048	valid
471.0ms	1415×	body	512	valid
217.0ms	1338×	body	128	valid
134.0ms	612×	body	256	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% 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

38.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.0b	(-.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
✓	1.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.5b	(tan.f64 (+.f64 x eps))

series65.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

39.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
26.0ms	(tan.f64 (+.f64 x eps))

rewrite55.0ms (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

Calls

2 calls:

52.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
52.0ms	(tan.f64 (+.f64 x eps))

simplify36.0ms (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

prune136.0ms (1.3%)

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

0.2b

Counts

148 → 9

Alt Table

Status	Error	Program
	23.7b	(/.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)))
	23.5b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	23.8b	(+.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))))
	32.6b	(+.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)))))))))
	23.6b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	32.2b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	23.5b	(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)))
	32.6b	(+.f64 (+.f64 (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)) (.f64 1/3 (pow.f64 eps 3)))) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (sin.f64 x) 4) 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)))))
	32.2b	(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.f64 x) 2) eps)

Compiler

Compiled 4053 to 1664 computations (58.9% 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))
✓	2.7b	(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)))

series280.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

127.0ms	(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)))
98.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
31.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
25.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite56.0ms (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

Calls

4 calls:

54.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
54.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
54.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
54.0ms	(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)))

simplify65.0ms (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

prune247.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	191	13	204

Error

0.1b

Counts

204 → 13

Alt Table

Status	Error	Program
	23.7b	(/.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)))
▶	23.5b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	23.8b	(+.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))))
	32.6b	(+.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)))))))))
	24.4b	(fma.f64 (pow.f64 (cbrt.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)))
	32.2b	(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.f64 x) 2) eps)
	43.2b	(fma.f64 (pow.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 3) 1/3) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	23.6b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	32.2b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	23.7b	(fma.f64 (/.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	23.7b	(-.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)))
	32.6b	(+.f64 (+.f64 (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)) (.f64 1/3 (pow.f64 eps 3)))) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (sin.f64 x) 4) 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)))))
	23.8b	(fma.f64 (fma.f64 (cbrt.f64 (tan.f64 x)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 6193 to 2630 computations (57.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.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))
✓	2.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

series325.0ms (3%)

Counts

2 → 48

Calls

2 calls:

199.0ms

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

126.0ms

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

rewrite65.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

279×	`fma-neg_binary64`
251×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
135×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	278	47
2	4023	47

Stop Event

1×	node limit

Counts

2 → 101

Calls

2 calls:

63.0ms

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

62.0ms

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

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
724×	`fma-def_binary64`
630×	`associate-/l*_binary64`
351×	`associate-/r*_binary64`
188×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	2870
1	393	2856
2	1507	2777

Stop Event

1×	node limit

Counts

149 → 133

prune311.0ms (2.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	240	6	246
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	248	11	259

Error

0.1b

Counts

259 → 11

Alt Table

Status	Error	Program
	23.6b	(fma.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (pow.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) -2))) (/.f64 1 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	32.6b	(+.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)))))))))
	23.6b	(-.f64 (.f64 (fma.f64 (sin.f64 x) (/.f64 1 (cos.f64 x)) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
▶	23.5b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	32.2b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	24.5b	(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 2) (pow.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 2)) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	23.7b	(-.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)))
	32.6b	(+.f64 (+.f64 (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)) (.f64 1/3 (pow.f64 eps 3)))) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (sin.f64 x) 4) 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 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 2))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
	24.5b	(fma.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) 2) (neg.f64 (tan.f64 x)))
	32.2b	(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.f64 x) 2) eps)

Compiler

Compiled 7941 to 3383 computations (57.4% saved)

localize13.0ms (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))
✓	2.7b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))

series130.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

129.0ms

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

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

353×	`fma-def_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
189×	`fma-neg_binary64`
138×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	295	26
2	3903	24

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

45.0ms

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

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
630×	`associate-/l*_binary64`
473×	`fma-def_binary64`
351×	`associate-/r*_binary64`
120×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1758
1	321	1752
2	1198	1707

Stop Event

1×	node limit

Counts

49 → 42

prune201.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	196	10	206

Error

0.1b

Counts

206 → 10

Alt Table

Status	Error	Program
	23.6b	(fma.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (pow.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) -2))) (/.f64 1 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	23.6b	(-.f64 (.f64 (fma.f64 (sin.f64 x) (/.f64 1 (cos.f64 x)) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	32.2b	(fma.f64 (/.f64 eps (pow.f64 (cos.f64 x) 2)) (pow.f64 (sin.f64 x) 2) eps)
	32.6b	(+.f64 (+.f64 (.f64 (/.f64 eps (/.f64 (cos.f64 x) eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))) (fma.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (cos.f64 x) 4)) (pow.f64 (sin.f64 x) 4) eps)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (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))))
✓	23.5b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	32.2b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	24.5b	(fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 2) (pow.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 2)) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	23.7b	(-.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)))
	23.5b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 2))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
	24.5b	(fma.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) 2) (neg.f64 (tan.f64 x)))

Compiler

Compiled 5952 to 2595 computations (56.4% saved)

regimes3.6s (32.8%)

Accuracy

Total 0.2b remaining (54.9%)

Threshold costs 0.2b (54.9%)

Counts

339 → 3

Compiler

Compiled 23967 to 14856 computations (38% saved)

bsearch104.0ms (1%)

Steps

Iters	Range		Point
10	1.6795503906626607e-12	0.09694508389703652	4.0929675985837755e-5
9	-33.33514890780328	-4.475775861958821e-5	-5.0008209901859945e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	181
1	76	181
2	90	181
3	105	181
4	114	181
5	118	181
6	119	181

Stop Event

1×

saturated

end253.0ms (2.3%)

Compiler: Compiled 561 to 330 computations (41.2% saved)

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	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

analyze1.2s (11.2%)

sample3.6s (32.8%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series65.0ms (0.6%)

rewrite55.0ms (0.5%)

simplify36.0ms (0.3%)

prune136.0ms (1.3%)

localize10.0ms (0.1%)

series280.0ms (2.6%)

rewrite56.0ms (0.5%)

simplify65.0ms (0.6%)

prune247.0ms (2.3%)

localize11.0ms (0.1%)

series325.0ms (3%)

rewrite65.0ms (0.6%)

simplify51.0ms (0.5%)

prune311.0ms (2.9%)

localize13.0ms (0.1%)

series130.0ms (1.2%)

rewrite46.0ms (0.4%)

simplify36.0ms (0.3%)

prune201.0ms (1.8%)

regimes3.6s (32.8%)

bsearch104.0ms (1%)

simplify8.0ms (0.1%)

end253.0ms (2.3%)

Profiling

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