Details

analyze1.1s (12.7%)

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)

sample115.0ms (1.3%)

Algorithm

1×

intervals

Results

36.0ms	43×	body	2048	valid
35.0ms	116×	body	1024	valid
8.0ms	44×	body	512	valid
3.0ms	22×	body	256	valid
2.0ms	31×	body	128	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify12.0ms (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

38.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.3b	(-.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
✓	1.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.1b	(tan.f64 (+.f64 x eps))

series83.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

51.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
32.0ms	(tan.f64 (+.f64 x eps))

rewrite13.0ms (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:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

simplify107.0ms (1.2%)

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

prune93.0ms (1%)

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
▶	23.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	32.4b	(+.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)))))))))))
	23.6b	(/.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)))))
	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)))
	31.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	32.4b	(+.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)))))

Compiler

Compiled 2931 to 1221 computations (58.3% 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 (tan.f64 x) (tan.f64 eps)) (-.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)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series454.0ms (5.1%)

Counts

4 → 96

Calls

4 calls:

268.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
114.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
28.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite45.0ms (0.5%)

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:

13.0ms	(-.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))

simplify281.0ms (3.2%)

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 (3.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	235	10	245
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	238	13	251

Error

0.1b

Counts

251 → 13

Alt Table

Status	Error	Program
	23.6b	(/.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)))))
	26.9b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) 3))
	41.7b	(+.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)))))
	31.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	23.6b	(-.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)))
	32.4b	(+.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)))))
▶	23.5b	(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)))
	23.5b	(-.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))
	25.3b	(/.f64 (-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))
	24.2b	(.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))))
	32.8b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	32.3b	(+.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 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
	24.1b	(+.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))

Compiler

Compiled 9721 to 3321 computations (65.8% saved)

localize11.0ms (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))
✓	3.1b	(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)))

series222.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

143.0ms	(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)))
78.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 45

Calls

2 calls:

3.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.0ms	(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)))

simplify87.0ms (1%)

Algorithm

1×	egg-herbie

Rules

942×	`associate-/l*_binary64`
649×	`fma-def_binary64`
456×	`associate-/r*_binary64`
176×	`associate-/r/_binary64`
160×	`unswap-sqr_binary64`

Counts

93 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	3516
1	505	3354
2	1728	3283
3	5194	3283

prune277.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	162	5	167
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	167	13	180

Error

0.1b

Counts

180 → 13

Alt Table

Status	Error	Program
	41.7b	(+.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)))))
	31.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	32.3b	(+.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 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
	27.2b	(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)))
	23.6b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	24.6b	(log1p.f64 (expm1.f64 (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)))))
	34.0b	(expm1.f64 (log1p.f64 (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)))))
	24.2b	(.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))))
	23.6b	(/.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)))))
▶	23.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (neg.f64 (tan.f64 x)))
	32.8b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	32.4b	(+.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)))))
	24.1b	(+.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))

Compiler

Compiled 5845 to 2393 computations (59.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series208.0ms (2.3%)

Counts

3 → 72

Calls

3 calls:

150.0ms

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

35.0ms

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

23.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 55

Calls

3 calls:

4.0ms

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

4.0ms

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

0.0ms

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

simplify151.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
647×	`associate-/r*_binary64`
373×	`associate-/r/_binary64`
331×	`associate-/l/_binary64`
180×	`associate-/l*_binary64`

Counts

127 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3968
1	657	3731
2	2337	3596
3	5514	3596

prune210.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	158	13	171

Error

0.1b

Counts

171 → 13

Alt Table

Status	Error	Program
	41.7b	(+.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)))))
	31.9b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	23.8b	(fma.f64 (/.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (neg.f64 (tan.f64 x)))
	24.6b	(log1p.f64 (expm1.f64 (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)))))
	34.0b	(expm1.f64 (log1p.f64 (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)))))
	12.9b	(+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) -1)))
	24.2b	(.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))))
	23.6b	(/.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)))))
✓	23.5b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (neg.f64 (tan.f64 x)))
	32.8b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	32.3b	(+.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 4/3 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
	32.4b	(+.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)))))
	24.1b	(+.f64 (fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (.f64 (cbrt.f64 (tan.f64 x)) (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))

Compiler

Compiled 5501 to 2067 computations (62.4% saved)

regimes2.0s (22.8%)

Accuracy

Total 0.3b remaining (71.1%)

Threshold costs 0.3b (71.1%)

Counts

295 → 3

Compiler

Compiled 26022 to 14414 computations (44.6% saved)

bsearch82.0ms (0.9%)

Steps

Iters	Range		Point
7	6.692656721251007e-15	4.1468436063748305e-13	4.0940859351585484e-13
10	-0.018492646506650032	-1.5207672419987833e-12	-0.00028767276362063015

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
18×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	296
1	120	296
2	130	296
3	137	296
4	141	296
5	142	296
6	140	296

end7.0ms (0.1%)

Compiler: Compiled 189 to 110 computations (41.8% saved)

sample2.9s (32.7%)

Algorithm

1×

intervals

Results

1.2s	3477×	body	1024	valid
717.0ms	1282×	body	2048	valid
281.0ms	1407×	body	512	valid
81.0ms	1256×	body	128	valid
71.0ms	575×	body	256	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 685 to 376 computations (45.1% 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

analyze1.1s (12.7%)

sample115.0ms (1.3%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series83.0ms (0.9%)

rewrite13.0ms (0.1%)

simplify107.0ms (1.2%)

prune93.0ms (1%)

localize13.0ms (0.1%)

series454.0ms (5.1%)

rewrite45.0ms (0.5%)

simplify281.0ms (3.2%)

prune306.0ms (3.4%)

localize11.0ms (0.1%)

series222.0ms (2.5%)

rewrite6.0ms (0.1%)

simplify87.0ms (1%)

prune277.0ms (3.1%)

localize15.0ms (0.2%)

series208.0ms (2.3%)

rewrite10.0ms (0.1%)

simplify151.0ms (1.7%)

prune210.0ms (2.4%)

regimes2.0s (22.8%)

bsearch82.0ms (0.9%)

simplify9.0ms (0.1%)

end7.0ms (0.1%)

sample2.9s (32.7%)

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