Details

analyze1.1s (13%)

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)

sample80.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	108×	body	1024	valid
23.0ms	37×	body	2048	valid
9.0ms	47×	body	512	valid
3.0ms	16×	body	256	valid
3.0ms	48×	body	128	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	21	11
4	27	11
5	42	11
6	65	11
7	78	11
8	90	11
9	92	11
10	86	11
11	72	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

37.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	37.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.9b	(tan.f64 (+.f64 x eps))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

20.9b

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
4×	`tan-quot_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

2 → 27

Calls

2 calls:

5.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 409 to 106 computations (74.1% saved)

series106.0ms (1.2%)

Error

14.2b

Counts

2 → 23

Calls

2 calls:

48.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
31.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1614 to 960 computations (40.5% saved)

simplify130.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

909×	`times-frac_binary64`
605×	`associate-/l*_binary64`
330×	`associate-/r*_binary64`
175×	`associate-+r+_binary64`
120×	`unswap-sqr_binary64`

Counts

50 → 31

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	179	1552
1	457	1529
2	1505	1475
3	4987	1466
4	4986	1457
5	4996	1454
6	4977	1454

prune35.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Error

0.4b

Counts

32 → 2

Alt Table

Status	Error	Program
▶	21.4b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	31.5b	(+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))

Status

Error

Program

▶

21.4b

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

31.5b

(+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))

Compiler

Compiled 887 to 387 computations (56.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
8.2b	(-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))

rewrite181.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

17×	`associate-*r/_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`tan-quot_binary64`
12×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64`

Counts

4 → 90

Calls

4 calls:

8.0ms	(-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
7.0ms	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3526 to 992 computations (71.9% saved)

series276.0ms (3.1%)

Error

0.1b

Counts

4 → 41

Calls

4 calls:

118.0ms	(-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
43.0ms	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))
39.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3762 to 1980 computations (47.4% saved)

simplify177.0ms (2%)

Algorithm

1×	egg-herbie

Rules

598×	`times-frac_binary64`
303×	`associate-l_binary64`
301×	`associate-r_binary64`
275×	`cancel-sign-sub-inv_binary64`
244×	`distribute-rgt-neg-in_binary64`

Counts

131 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3480
1	787	3377
2	2928	3353
3	4401	3353
4	4976	3353
5	4966	3353

prune150.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	11	77
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Error

0.1b

Counts

79 → 12

Alt Table

Status	Error	Program
	31.5b	(+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))
	25.4b	(/.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) 3) (pow.f64 (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (+.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.4b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(/.f64 (+.f64 (.f64 1/3 (.f64 (cos.f64 x) (pow.f64 eps 3))) (+.f64 (.f64 17/315 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (pow.f64 eps 7))) (+.f64 (.f64 1/3 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (pow.f64 eps 3))) (+.f64 (.f64 eps (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (+.f64 (.f64 2/15 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (pow.f64 eps 5))) (.f64 (cos.f64 x) (+.f64 (.f64 2/15 (pow.f64 eps 5)) (.f64 17/315 (pow.f64 eps 7))))))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
▶	0.5b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.4b	(/.f64 (-.f64 (+.f64 (.f64 (cos.f64 x) (tan.f64 x)) (.f64 (cos.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.5b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (.f64 (tan.f64 eps) (cbrt.f64 (tan.f64 x))))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	20.1b	(/.f64 (-.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)) (.f64 (neg.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	21.8b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (cos.f64 x)))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	23.2b	(/.f64 (/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (-.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))))) (.f64 (.f64 (sin.f64 x) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.5b	(/.f64 (/.f64 (.f64 (cos.f64 x) (-.f64 (.f64 (+.f64 (.f64 (sin.f64 eps) (cos.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 eps) (.f64 (sin.f64 x) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps)))))))) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	21.5b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))

Compiler

Compiled 3677 to 1444 computations (60.7% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(pow.f64 (sin.f64 x) 2)

rewrite177.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 89

Calls

4 calls:

20.0ms	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
17.0ms	(.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps))))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 3635 to 1210 computations (66.7% saved)

series264.0ms (3%)

Error

0.1b

Counts

4 → 32

Calls

4 calls:

117.0ms	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
68.0ms	(.f64 (sin.f64 eps) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps))))
41.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
7.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 2982 to 1654 computations (44.5% saved)

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

465×	`distribute-rgt-in_binary64`
297×	`times-frac_binary64`
270×	`unswap-sqr_binary64`
239×	`associate-l_binary64`
229×	`associate-/l*_binary64`

Counts

121 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4549
1	853	3844
2	3495	3797
3	5400	3797

prune117.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	87	15	102

Error

0.0b

Counts

102 → 15

Alt Table

Status	Error	Program
	0.5b	(/.f64 (sin.f64 eps) (/.f64 (cos.f64 x) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))
	0.8b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 (/.f64 (.f64 (sin.f64 eps) (.f64 (cos.f64 eps) 1)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 eps)) (.f64 (.f64 (cos.f64 eps) (cos.f64 x)) (cos.f64 x)))) (.f64 (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (pow.f64 (cos.f64 eps) 2))))
	31.5b	(+.f64 eps (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))
	25.4b	(/.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) 3) (pow.f64 (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (+.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.8b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (cos.f64 x)))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	19.4b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) 3)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	1.0b	(/.f64 (.f64 (.f64 (sin.f64 eps) (.f64 (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps)))))) (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 6)) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (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))))))
	0.7b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) 3) (pow.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) 3))) (.f64 (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (/.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (cos.f64 eps)) (cos.f64 eps)) (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps)))))))
▶	0.4b	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))) (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))
	21.5b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))

Compiler

Compiled 4049 to 1740 computations (57% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(pow.f64 (sin.f64 x) 2)
0.3b	(*.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))

rewrite198.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`
16×	`associate-l_binary64`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
7.0ms	(*.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 4209 to 1299 computations (69.1% saved)

series334.0ms (3.8%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

128.0ms	(*.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))
119.0ms	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
37.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
7.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 3259 to 1720 computations (47.2% saved)

simplify169.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

296×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`
248×	`unswap-sqr_binary64`
229×	`associate-l_binary64`
212×	`associate-r_binary64`

Counts

132 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	4163
1	829	3704
2	2823	3333
3	4910	3333
4	4998	3333
5	4970	3333

prune136.0ms (1.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	96	15	111

Error

0.0b

Counts

111 → 15

Alt Table

Status	Error	Program
	0.8b	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 x) (cos.f64 eps))) (cbrt.f64 (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (sin.f64 eps) (cbrt.f64 (/.f64 (cos.f64 x) (cos.f64 eps)))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.4b	(.f64 (/.f64 1 (cos.f64 x)) (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 (sin.f64 eps) (/.f64 (cos.f64 x) (/.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))
	0.8b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 x)) 4) (pow.f64 (cbrt.f64 (sin.f64 x)) 2)) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	21.8b	(/.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (cos.f64 x)))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.4b	(/.f64 (+.f64 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))))
	19.4b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) 3)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.4b	(.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 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))))
	21.5b	(/.f64 (-.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))))
	0.5b	(/.f64 (+.f64 (.f64 (.f64 (pow.f64 (sin.f64 x) 2) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 eps)) (.f64 (cos.f64 x) (.f64 (cos.f64 x) (sin.f64 eps)))) (.f64 (cos.f64 eps) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (pow.f64 (cos.f64 x) 2))))
	1.0b	(/.f64 (.f64 (.f64 (sin.f64 eps) (.f64 (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps)))) (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps)))))) (cbrt.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 eps) (cos.f64 x))) (/.f64 (cos.f64 x) (cos.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	0.4b	(/.f64 (+.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 6)) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (/.f64 (cos.f64 x) (cos.f64 eps)) (sin.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	25.4b	(/.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) 3) (pow.f64 (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (+.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (sin.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))))) (cbrt.f64 (/.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (cos.f64 x) (cos.f64 eps))) (sin.f64 eps)) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))))
	0.4b	(.f64 (/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (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))))))

Compiler

Compiled 3684 to 1426 computations (61.3% saved)

regimes1.8s (20.4%)

Accuracy

Total 0.4b remaining (88.3%)

Threshold costs 0.4b (88.3%)

Compiler

Compiled 46362 to 25563 computations (44.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	54
1	33	54
2	42	54
3	48	54
4	52	54
5	53	54
6	52	54

end2.0ms (0%)

Compiler: Compiled 35 to 20 computations (42.9% saved)

sample3.1s (34.9%)

Algorithm

1×

intervals

Results

1.2s	3617×	body	1024	valid
680.0ms	1181×	body	2048	valid
319.0ms	1349×	body	512	valid
84.0ms	585×	body	256	valid
83.0ms	1268×	body	128	valid

Compiler

Compiled 776 to 412 computations (46.9% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	21	11
4	27	11
5	42	11
6	65	11
7	78	11
8	90	11
9	92	11
10	86	11
11	72	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	21	11
4	27	11
5	42	11
6	65	11
7	78	11
8	90	11
9	92	11
10	86	11
11	72	11

Details

analyze1.1s (13%)

sample80.0ms (0.9%)

simplify15.0ms (0.2%)

prune1.0ms (0%)

localize7.0ms (0.1%)

rewrite33.0ms (0.4%)

series106.0ms (1.2%)

simplify130.0ms (1.5%)

prune35.0ms (0.4%)

localize18.0ms (0.2%)

rewrite181.0ms (2.1%)

series276.0ms (3.1%)

simplify177.0ms (2%)

prune150.0ms (1.7%)

localize24.0ms (0.3%)

rewrite177.0ms (2%)

series264.0ms (3%)

simplify121.0ms (1.4%)

prune117.0ms (1.3%)

localize30.0ms (0.3%)

rewrite198.0ms (2.3%)

series334.0ms (3.8%)

simplify169.0ms (1.9%)

prune136.0ms (1.5%)

regimes1.8s (20.4%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample3.1s (34.9%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	21	11
4	27	11
5	42	11
6	65	11
7	78	11
8	90	11
9	92	11
10	86	11
11	72	11