Details

analyze1.2s (10.6%)

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)

sample117.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	98×	body	1024	valid
22.0ms	46×	body	2048	valid
21.0ms	55×	body	512	valid
3.0ms	45×	body	128	valid
2.0ms	12×	body	256	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

38.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.2b	(-.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
✓	1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.9b	(tan.f64 (+.f64 x eps))

series79.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

50.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
29.0ms	(tan.f64 (+.f64 x eps))

rewrite10.0ms (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))

simplify109.0ms (1%)

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

prune104.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

0.2b

Counts

94 → 9

Alt Table

Status	Error	Program
	20.7b	(/.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)))
	31.7b	(fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (/.f64 (sin.f64 eps) (cos.f64 eps)))
▶	20.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	42.1b	(-.f64 (expm1.f64 (log1p.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
	32.2b	(+.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)))))
	32.2b	(+.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)))))))))))
	31.7b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	31.7b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	20.7b	(/.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 3157 to 1365 computations (56.8% 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))
✓	2.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series456.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

213.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
176.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
36.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
30.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite51.0ms (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 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
11.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify290.0ms (2.6%)

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

prune326.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	237	8	245
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	242	12	254

Error

0.1b

Counts

254 → 12

Alt Table

Status	Error	Program
	21.8b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	45.1b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.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))))))
	32.2b	(+.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)))))))))))
	20.7b	(-.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)))
	31.7b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.2b	(+.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 (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))))))
	21.0b	(-.f64 (/.f64 (fma.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶	20.5b	(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)))
	32.2b	(+.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)))))
	20.8b	(/.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)))))
	31.7b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	20.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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))) 0)

Compiler

Compiled 9919 to 3437 computations (65.3% saved)

localize14.0ms (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))
✓	2.2b	(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)))

series242.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

149.0ms	(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)))
93.0ms	(/.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)))

simplify80.0ms (0.7%)

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

prune311.0ms (2.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	165	14	179

Error

0.1b

Counts

179 → 14

Alt Table

Status	Error	Program
	21.8b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	45.1b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.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))))))
	32.2b	(+.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)))))))))))
	20.7b	(-.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)))
	31.7b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.2b	(+.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 (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))))))
	21.0b	(-.f64 (/.f64 (fma.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	20.5b	(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)))
	21.3b	(.f64 (.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))))
	20.8b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 1 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	32.2b	(+.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)))))
	20.8b	(/.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)))))
	31.7b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
▶	20.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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))) 0)

Compiler

Compiled 6311 to 2607 computations (58.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	2.1b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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)))

series1.1s (9.5%)

Counts

3 → 72

Calls

3 calls:

643.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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)))

334.0ms

(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))

78.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
20×	`difference-of-squares_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 100

Calls

3 calls:

8.0ms

(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))

4.0ms

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

0.0ms

(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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)))

simplify197.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

385×	`unswap-sqr_binary64`
292×	`times-frac_binary64`
217×	`associate-/l*_binary64`
202×	`associate-r_binary64`
191×	`associate-l_binary64`

Counts

172 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	11027
1	859	10697
2	3727	10572
3	5049	10572

prune451.0ms (4.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	240	15	255

Error

0.1b

Counts

255 → 15

Alt Table

Status	Error	Program
	21.8b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	45.1b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.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))))))
	32.2b	(+.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)))))))))))
	20.7b	(-.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)))
	32.2b	(+.f64 (+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (/.f64 (.f64 (sin.f64 x) (.f64 eps eps)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (+.f64 (/.f64 (.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.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)) (+.f64 (.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (fma.f64 (pow.f64 eps 3) 1/3 (.f64 2/3 (/.f64 (.f64 (sin.f64 x) (pow.f64 eps 4)) (cos.f64 x)))))))))))) 0)
	20.8b	(/.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)))))
	31.7b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.2b	(+.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 (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))))))
	43.2b	(+.f64 (fma.f64 (exp.f64 (log.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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))) 0)
	21.0b	(-.f64 (/.f64 (fma.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	20.5b	(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)))
	21.3b	(.f64 (.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))))
	20.8b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 1 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	31.7b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
✓	20.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.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))) 0)

Compiler

Compiled 12417 to 5154 computations (58.5% saved)

regimes2.7s (24.1%)

Accuracy

Total 0.5b remaining (80.3%)

Threshold costs 0.5b (80.3%)

Counts

287 → 3

Compiler

Compiled 26749 to 14673 computations (45.1% saved)

bsearch86.0ms (0.8%)

Steps

Iters	Range		Point
8	5.719672698916291e-25	1.9456980262931857e-22	1.9282140589339793e-22
9	-18.768436733555312	-6.868851198653264e-5	-0.0002726995289715794

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
16×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	281
1	113	281
2	121	281
3	126	281
4	128	281
5	127	281

end3.0ms (0%)

Compiler: Compiled 180 to 108 computations (40% saved)

sample3.2s (28.5%)

Algorithm

1×

intervals

Results

1.2s	3433×	body	1024	valid
767.0ms	1262×	body	2048	valid
313.0ms	1360×	body	512	valid
100.0ms	1360×	body	128	valid
83.0ms	584×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 938 to 502 computations (46.5% 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 (10.6%)

sample117.0ms (1.1%)

simplify12.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series79.0ms (0.7%)

rewrite10.0ms (0.1%)

simplify109.0ms (1%)

prune104.0ms (0.9%)

localize10.0ms (0.1%)

series456.0ms (4.1%)

rewrite51.0ms (0.5%)

simplify290.0ms (2.6%)

prune326.0ms (2.9%)

localize14.0ms (0.1%)

series242.0ms (2.2%)

rewrite6.0ms (0.1%)

simplify80.0ms (0.7%)

prune311.0ms (2.8%)

localize19.0ms (0.2%)

series1.1s (9.5%)

rewrite22.0ms (0.2%)

simplify197.0ms (1.8%)

prune451.0ms (4.1%)

regimes2.7s (24.1%)

bsearch86.0ms (0.8%)

simplify8.0ms (0.1%)

end3.0ms (0%)

sample3.2s (28.5%)

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