Details

analyze1.2s (10.8%)

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)

sample3.7s (32.5%)

Results

1.8s	3569×	body	1024	valid
1.0s	1254×	body	2048	valid
487.0ms	1415×	body	512	valid
184.0ms	1367×	body	128	valid
154.0ms	651×	body	256	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

33.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.5b	(-.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))
✓	3.2b	(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))
30.0ms	(tan.f64 (+.f64 x eps))

rewrite116.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

883×	`prod-diff_binary64`
412×	`fma-def_binary64`
215×	`fma-neg_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

2 → 117

Calls

2 calls:

113.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
113.0ms	(tan.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	169	17
2	2430	17
3	4853	17
4	4989	17
5	4989	17
0	0	0
1	0	0

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

165 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1638
1	363	1636
2	1362	1545
3	5021	1545

prune147.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Error

0.1b

Counts

148 → 8

Alt Table

Status	Error	Program
	18.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	28.2b	(fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 (.f64 x x) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (sin.f64 eps) (cos.f64 eps))))))
	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 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)))))
▶	18.5b	(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)))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	18.6b	(/.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 (.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)))))))))))
	18.8b	(+.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))))

Compiler

Compiled 4193 to 1758 computations (58.1% 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))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.5b	(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)))

series319.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

159.0ms	(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)))
92.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
37.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
31.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite97.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

332×	`fma-def_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
191×	`log-pow_binary64`
186×	`fma-neg_binary64`

Counts

4 → 153

Calls

4 calls:

94.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
94.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
94.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
94.0ms	(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	59
1	265	56
2	3080	52
3	5000	52
4	4966	52
0	0	0
1	0	0

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

249 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3402
1	527	3386
2	1815	3309
3	5279	3309

prune343.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	6	215
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	213	10	223

Error

0.1b

Counts

223 → 10

Alt Table

Status	Error	Program
	19.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (pow.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 2)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	18.5b	(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)))
	28.7b	(fma.f64 (log.f64 (.f64 (+.f64 1 (expm1.f64 (tan.f64 x))) (exp.f64 (tan.f64 eps)))) (/.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 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)))))
	18.6b	(-.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)))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	23.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (fma.f64 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) -1))) (neg.f64 (tan.f64 x)))
▶	18.5b	(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)))
	18.6b	(/.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 (.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)))))))))))

Compiler

Compiled 6667 to 2814 computations (57.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.5b	(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)))

series591.0ms (5.2%)

Counts

2 → 48

Calls

2 calls:

513.0ms

(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)))

78.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

rewrite73.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 65

Calls

2 calls:

71.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)

71.0ms

(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	370	60
2	4261	60
3	5022	60
0	0	0
1	0	0

simplify133.0ms (1.2%)

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`

Counts

113 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	7148
1	497	7046
2	2455	6245
3	5150	6245

prune641.0ms (5.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	274	3	277
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	276	11	287

Error

0.1b

Counts

287 → 11

Alt Table

Status	Error	Program
	19.0b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (log1p.f64 (expm1.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)))
	23.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (fma.f64 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) -1))) (neg.f64 (tan.f64 x)))
	19.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (pow.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 2)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	18.5b	(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)))
	33.2b	(+.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 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)))))
▶	18.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 9)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	18.6b	(-.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)))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	18.6b	(/.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 (.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)))))))))))
	18.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) 2) (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 2))))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))

Compiler

Compiled 13346 to 5725 computations (57.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.5b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9)
✓	2.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 9)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
✓	7.6b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9))

series870.0ms (7.7%)

Counts

3 → 72

Calls

3 calls:

600.0ms

(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (/.f64 1 (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))

185.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9)

85.0ms

(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9))

rewrite78.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

322×	`log1p-udef_binary64`
191×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
181×	`add-cbrt-cube_binary64`

Counts

3 → 75

Calls

3 calls:

76.0ms

(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9)

76.0ms

(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (/.f64 1 (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))

76.0ms

(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 9))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
1	392	71
2	4602	71
3	4994	71
0	0	0
1	0	0

simplify204.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
380×	`unswap-sqr_binary64`
273×	`times-frac_binary64`
212×	`associate-/l*_binary64`
171×	`associate-r_binary64`

Counts

147 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	8074
1	647	7962
2	3058	7161
3	4991	7161
4	4988	7161
5	4956	7161

prune426.0ms (3.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	228	11	239

Error

0.0b

Counts

239 → 11

Alt Table

Status	Error	Program
	19.0b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (log1p.f64 (expm1.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)))
	23.1b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (fma.f64 (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) (sqrt.f64 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) -1))) (neg.f64 (tan.f64 x)))
	19.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (pow.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 2)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	18.5b	(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)))
	33.2b	(+.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 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)))))
✓	18.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 9)))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1)) (neg.f64 (tan.f64 x)))
	18.6b	(-.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)))
	32.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	20.7b	(/.f64 (-.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)))) (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))))) (pow.f64 (tan.f64 x) 2)) (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (fma.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (tan.f64 x)))
	18.6b	(/.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 (.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)))))))))))

Compiler

Compiled 11428 to 5127 computations (55.1% saved)

regimes1.6s (14.4%)

Accuracy

Total 0.2b remaining (55.4%)

Threshold costs 0.2b (55.4%)

Counts

262 → 3

Compiler

Compiled 23094 to 13842 computations (40.1% saved)

bsearch93.0ms (0.8%)

Steps

Iters	Range		Point
9	7.976258469646053e-6	20.70803440592603	2.0641519632213958e-5
8	-0.09787255974932453	-4.4150859714864385e-5	-5.0115677135327515e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	174
1	72	174
2	84	174
3	91	174
4	95	174
5	96	174
6	95	174

end353.0ms (3.1%)

Compiler: Compiled 797 to 452 computations (43.3% 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 (10.8%)

sample3.7s (32.5%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series77.0ms (0.7%)

rewrite116.0ms (1%)

simplify47.0ms (0.4%)

prune147.0ms (1.3%)

localize10.0ms (0.1%)

series319.0ms (2.8%)

rewrite97.0ms (0.9%)

simplify79.0ms (0.7%)

prune343.0ms (3%)

localize17.0ms (0.2%)

series591.0ms (5.2%)

rewrite73.0ms (0.7%)

simplify133.0ms (1.2%)

prune641.0ms (5.7%)

localize18.0ms (0.2%)

series870.0ms (7.7%)

rewrite78.0ms (0.7%)

simplify204.0ms (1.8%)

prune426.0ms (3.8%)

regimes1.6s (14.4%)

bsearch93.0ms (0.8%)

simplify6.0ms (0.1%)

end353.0ms (3.1%)

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