Details

analyze1.2s (5.9%)

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)

sample3.7s (17.4%)

Results

1.9s	3679×	body	1024	valid
946.0ms	1245×	body	2048	valid
485.0ms	1440×	body	512	valid
184.0ms	1287×	body	128	valid
141.0ms	602×	body	256	valid
4.0ms	3×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (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

38.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.9b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize99.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.0b	(tan.f64 (+.f64 x eps))

series76.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
29.0ms	(tan.f64 (+.f64 x eps))

rewrite11.0ms (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))

simplify107.0ms (0.5%)

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

prune164.0ms (0.8%)

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
	25.3b	(/.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)))
	29.6b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	30.1b	(+.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)))))
	30.1b	(+.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)))))))))))
▶	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	25.3b	(/.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)))))
	29.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 3099 to 1327 computations (57.2% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 1 (*.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))))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series435.0ms (2%)

Counts

4 → 96

Calls

4 calls:

218.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
145.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
38.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
33.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

rewrite44.0ms (0.2%)

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:

12.0ms	(-.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))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify312.0ms (1.5%)

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

prune344.0ms (1.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	244	12	256
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	248	15	263

Error

0.1b

Counts

263 → 15

Alt Table

Status	Error	Program
▶	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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))))) (tan.f64 x))
	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (tan.f64 eps) (tan.f64 x)))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) (.f64 (tan.f64 eps) (tan.f64 x))))) (tan.f64 x))
	25.3b	(/.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)))))
	30.0b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	25.1b	(-.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))
	29.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	26.9b	(-.f64 (/.f64 (-.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	26.9b	(/.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)))
	44.2b	(+.f64 (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 (.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)))))
	25.8b	(+.f64 (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 (.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))))))
	30.1b	(+.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)))))
	31.7b	(log.f64 (/.f64 (exp.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (exp.f64 (tan.f64 x))))
	25.1b	(+.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)
	25.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (.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))
	30.1b	(+.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))))))))

Compiler

Compiled 10460 to 3673 computations (64.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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)))))
	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.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))))) (tan.f64 x))

series1.7s (8%)

Counts

3 → 72

Calls

3 calls:

1.3s

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

349.0ms

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

62.0ms

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

rewrite193.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

615×	`times-frac_binary64`
528×	`*-un-lft-identity_binary64`
353×	`add-sqr-sqrt_binary64`
344×	`add-cube-cbrt_binary64`
231×	`prod-diff_binary64`

Counts

3 → 494

Calls

3 calls:

35.0ms

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

16.0ms

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

7.0ms

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

simplify545.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
396×	`associate-r_binary64`
308×	`associate-/l*_binary64`
229×	`associate-*l/_binary64`
210×	`associate-/r/_binary64`

Counts

566 → 600

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	675	42679
1	1485	37519
2	5212	37519

prune1.1s (5.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	728	4	732
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	735	12	747

Error

0.1b

Counts

747 → 12

Alt Table

Status	Error	Program
	25.3b	(/.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)))))
	30.0b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	25.2b	(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (cbrt.f64 (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))))) (/.f64 (cbrt.f64 (-.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))))) (tan.f64 x))
	30.1b	(+.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))))))))
▶	25.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (tan.f64 eps))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))))) (tan.f64 x))
	25.2b	(fma.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps)))))) 1)) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (cbrt.f64 (-.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 (tan.f64 x)))
	30.1b	(+.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)))))
	31.7b	(log.f64 (/.f64 (exp.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (exp.f64 (tan.f64 x))))
	25.1b	(+.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)
	25.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (.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))
	29.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 45103 to 14243 computations (68.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (tan.f64 eps))
✓	0.2b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x))
	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (tan.f64 x)) (tan.f64 eps))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

series1.5s (7.2%)

Counts

3 → 72

Calls

3 calls:

1.4s

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

76.0ms

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

71.0ms

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

rewrite151.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

387×	`times-frac_binary64`
369×	`*-un-lft-identity_binary64`
256×	`add-sqr-sqrt_binary64`
247×	`add-cube-cbrt_binary64`
195×	`prod-diff_binary64`

Counts

3 → 346

Calls

3 calls:

34.0ms

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

9.0ms

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

5.0ms

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

simplify563.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-l_binary64`
385×	`associate-r_binary64`
200×	`associate-/l*_binary64`
171×	`associate-*l/_binary64`
167×	`fma-neg_binary64`

Counts

418 → 425

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	606	31669
1	1300	26578
2	4869	26578
3	4985	26578

prune794.0ms (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	512	1	513
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	514	11	525

Error

0.1b

Counts

525 → 11

Alt Table

Status	Error	Program
	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))))))) (tan.f64 x))
	25.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.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))
	25.3b	(/.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)))))
	30.0b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 (pow.f64 eps 3) 1/3)))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
	25.2b	(fma.f64 (/.f64 1 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps)))))) 1)) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (cbrt.f64 (-.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 (tan.f64 x)))
	30.1b	(+.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)))))
	31.7b	(log.f64 (/.f64 (exp.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (exp.f64 (tan.f64 x))))
	25.1b	(+.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)
	25.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (.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))
	30.1b	(+.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))))))))
	29.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 31838 to 10152 computations (68.1% saved)

regimes7.6s (35.9%)

Accuracy

Total 0.2b remaining (56.3%)

Threshold costs 0.2b (56.3%)

Counts

506 → 3

Compiler

Compiled 60993 to 30566 computations (49.9% saved)

bsearch118.0ms (0.6%)

Steps

Iters	Range		Point
8	3.801044519163615e-8	0.0007017592945067674	5.704032184871116e-5
11	-81572.5054599604	-3.73734481491823e-27	-4.798181894578827e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
15×	`*-commutative_binary64`
11×	`sub-neg_binary64`
7×	`distribute-rgt-neg-in_binary64`
7×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	235
1	85	235
2	108	235
3	126	235
4	135	235
5	137	235
6	135	235

end310.0ms (1.5%)

Compiler: Compiled 851 to 448 computations (47.4% 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 (5.9%)

sample3.7s (17.4%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize99.0ms (0.5%)

series76.0ms (0.4%)

rewrite11.0ms (0.1%)

simplify107.0ms (0.5%)

prune164.0ms (0.8%)

localize10.0ms (0%)

series435.0ms (2%)

rewrite44.0ms (0.2%)

simplify312.0ms (1.5%)

prune344.0ms (1.6%)

localize13.0ms (0.1%)

series1.7s (8%)

rewrite193.0ms (0.9%)

simplify545.0ms (2.6%)

prune1.1s (5.4%)

localize14.0ms (0.1%)

series1.5s (7.2%)

rewrite151.0ms (0.7%)

simplify563.0ms (2.7%)

prune794.0ms (3.7%)

regimes7.6s (35.9%)

bsearch118.0ms (0.6%)

simplify7.0ms (0%)

end310.0ms (1.5%)

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