Details

analyze1.2s (9%)

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)

sample3.9s (27.8%)

Results

1.9s	3587×	body	1024	valid
1.0s	1270×	body	2048	valid
610.0ms	1534×	body	512	valid
166.0ms	1274×	body	128	valid
145.0ms	591×	body	256	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify10.0ms (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

36.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.7b	(tan.f64 (+.f64 x eps))

series81.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

54.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
27.0ms	(tan.f64 (+.f64 x eps))

rewrite16.0ms (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:

12.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

simplify158.0ms (1.1%)

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

prune101.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	7	94

Error

0.2b

Counts

94 → 7

Alt Table

Status	Error	Program
	20.2b	(/.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)))
	37.9b	(-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 x 3)) (pow.f64 (cos.f64 eps) 2)) (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 3)) (.f64 x x) x) (.f64 (pow.f64 x 3) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 4) (pow.f64 (cos.f64 eps) 4)) 1/3))))) (tan.f64 x))
	33.1b	(+.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)))))
	33.3b	(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	33.0b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	20.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	20.2b	(/.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 3067 to 1289 computations (58% saved)

localize9.0ms (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 (tan.f64 x) (tan.f64 eps))))
✓	0.1b	(-.f64 1 (*.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 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series423.0ms (3%)

Counts

4 → 96

Calls

4 calls:

197.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
122.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
71.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
32.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
57×	`prod-diff_binary64`

Counts

4 → 173

Calls

4 calls:

14.0ms	(-.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))))
3.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify358.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

257×	`distribute-rgt-in_binary64`
212×	`unswap-sqr_binary64`
209×	`associate-+r+_binary64`
205×	`cancel-sign-sub-inv_binary64`
205×	`fma-neg_binary64`

Counts

269 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	383	10894
1	912	9239
2	3188	8700
3	4794	8700
4	4984	8700
5	4992	8700
6	4929	8700

prune299.0ms (2.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	246	10	256
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	250	13	263

Error

0.1b

Counts

263 → 13

Alt Table

Status	Error	Program
	33.1b	(+.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)))))
	24.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (expm1.f64 (log1p.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	20.1b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.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 (tan.f64 x)))
	20.2b	(-.f64 (/.f64 (/.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)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	33.0b	(+.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))))))))
	41.2b	(exp.f64 (log.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
▶	20.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
	21.1b	(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
	24.6b	(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (.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)))) (+.f64 (tan.f64 x) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))))))
	21.1b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	33.0b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.1b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	20.2b	(/.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 10120 to 3539 computations (65% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
✓	0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
✓	0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
✓	2.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

series260.0ms (1.9%)

Counts

4 → 80

Calls

4 calls:

206.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
35.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
9.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
9.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

rewrite65.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`*-un-lft-identity_binary64`
140×	`add-sqr-sqrt_binary64`
98×	`times-frac_binary64`
90×	`prod-diff_binary64`
83×	`add-cube-cbrt_binary64`

Counts

4 → 207

Calls

4 calls:

17.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
5.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
4.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

simplify281.0ms (2%)

Algorithm

1×	egg-herbie

Rules

327×	`times-frac_binary64`
271×	`associate-r_binary64`
246×	`associate-l_binary64`
246×	`fma-neg_binary64`
210×	`associate-/l*_binary64`

Counts

287 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	440	14275
1	1052	11053
2	4153	10298
3	4663	10298
4	4980	10298

prune336.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	290	3	293
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	294	12	306

Error

0.1b

Counts

306 → 12

Alt Table

Status	Error	Program
	21.2b	(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 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (neg.f64 (tan.f64 x)))
	41.2b	(exp.f64 (log.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	33.1b	(+.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)))))
▶	20.1b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.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 (tan.f64 x)))
	20.2b	(/.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)))))
	21.1b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (neg.f64 (tan.f64 x)))
	20.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 eps) (sin.f64 x)) 3)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
	33.0b	(+.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))))))))
	21.1b	(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
	24.6b	(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (.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)))) (+.f64 (tan.f64 x) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))))))
	33.0b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	21.1b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 13568 to 3825 computations (71.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	0.4b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	2.7b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.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 (tan.f64 x)))

series646.0ms (4.6%)

Counts

3 → 72

Calls

3 calls:

511.0ms

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

75.0ms

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

59.0ms

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

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`pow1_binary64`
36×	`tan-quot_binary64`
18×	`frac-times_binary64`
18×	`pow-prod-down_binary64`
18×	`add-cbrt-cube_binary64`

Counts

3 → 88

Calls

3 calls:

7.0ms

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

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

simplify172.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

615×	`unswap-sqr_binary64`
363×	`associate-r_binary64`
357×	`associate-l_binary64`
338×	`times-frac_binary64`
231×	`associate-/l*_binary64`

Counts

160 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	9212
1	883	8844
2	4096	8446
3	5520	8446

prune733.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	329	4	333
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	333	12	345

Error

0.1b

Counts

345 → 12

Alt Table

Status	Error	Program
	33.0b	(+.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))))))))
	21.3b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 2))) (.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	20.1b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (/.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 eps)) 3) (pow.f64 (cos.f64 x) 3)))) (+.f64 (.f64 1 1) (+.f64 (.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 (tan.f64 x)))
	33.0b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	22.4b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (log.f64 (exp.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))))) (+.f64 (.f64 1 1) (+.f64 (.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 (tan.f64 x)))
	20.2b	(/.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)))))
	21.1b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (neg.f64 (tan.f64 x)))
	21.2b	(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 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (neg.f64 (tan.f64 x)))
	33.1b	(+.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)))))
	21.1b	(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
	24.6b	(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (.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)))) (+.f64 (tan.f64 x) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))))))
	20.2b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 2)) (.f64 (pow.f64 (cos.f64 eps) 2) (.f64 (pow.f64 (cos.f64 x) 3) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))))) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))))) (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))) (+.f64 (/.f64 (.f64 (sin.f64 x) (pow.f64 (sin.f64 eps) 2)) (.f64 (pow.f64 (cos.f64 eps) 2) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3))))))) (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (sin.f64 eps)) (.f64 (cos.f64 eps) (.f64 (pow.f64 (cos.f64 x) 2) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (sin.f64 eps) 3)) (.f64 (pow.f64 (cos.f64 eps) 3) (pow.f64 (cos.f64 x) 3)))))))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

Compiler

Compiled 19274 to 7628 computations (60.4% saved)

regimes4.2s (29.8%)

Accuracy

Total 0.2b remaining (63.9%)

Threshold costs 0.2b (63.9%)

Counts

419 → 3

Compiler

Compiled 45660 to 25061 computations (45.1% saved)

bsearch120.0ms (0.9%)

Steps

Iters	Range		Point
7	1.6697837731345264e-5	0.001649469570201191	0.0002654352846451175
11	-0.000646807873129523	-7.236678228296966e-30	-9.830087725539631e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
14×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	272
1	103	272
2	114	272
3	123	272
4	135	272
5	142	272
6	147	272
7	149	272
8	146	272

end469.0ms (3.4%)

Compiler: Compiled 1133 to 638 computations (43.7% 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	79	272
1	103	272
2	114	272
3	123	272
4	135	272
5	142	272
6	147	272
7	149	272
8	146	272

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	79	272
1	103	272
2	114	272
3	123	272
4	135	272
5	142	272
6	147	272
7	149	272
8	146	272

Details

analyze1.2s (9%)

sample3.9s (27.8%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0%)

series81.0ms (0.6%)

rewrite16.0ms (0.1%)

simplify158.0ms (1.1%)

prune101.0ms (0.7%)

localize9.0ms (0.1%)

series423.0ms (3%)

rewrite45.0ms (0.3%)

simplify358.0ms (2.6%)

prune299.0ms (2.1%)

localize18.0ms (0.1%)

series260.0ms (1.9%)

rewrite65.0ms (0.5%)

simplify281.0ms (2%)

prune336.0ms (2.4%)

localize19.0ms (0.1%)

series646.0ms (4.6%)

rewrite17.0ms (0.1%)

simplify172.0ms (1.2%)

prune733.0ms (5.3%)

regimes4.2s (29.8%)

bsearch120.0ms (0.9%)

simplify11.0ms (0.1%)

end469.0ms (3.4%)

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

Iter	Nodes	Cost
0	79	272
1	103	272
2	114	272
3	123	272
4	135	272
5	142	272
6	147	272
7	149	272
8	146	272