Details

analyze2.1s (10.1%)

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)

sample158.0ms (0.8%)

Algorithm

1×

intervals

Results

69.0ms	117×	body	1024	valid
45.0ms	41×	body	2048	valid
14.0ms	35×	body	512	valid
9.0ms	19×	body	256	valid
5.0ms	44×	body	128	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify31.0ms (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

prune3.0ms (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

37.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.4b	(tan.f64 (+.f64 x eps))

rewrite23.0ms (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:

13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series270.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

174.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
96.0ms	(tan.f64 (+.f64 x eps))

simplify218.0ms (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 → 138

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

prune283.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	132	6	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Error

0.2b

Counts

139 → 6

Alt Table

Status	Error	Program
	31.2b	(+.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)))))
	23.1b	(/.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)))
	31.1b	(+.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)))))))))))
	30.8b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
▶	22.8b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	23.0b	(/.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 3074 to 1303 computations (57.6% saved)

localize23.0ms (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 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	3.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite167.0ms (0.8%)

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:

25.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
13.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
8.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series1.8s (8.8%)

Counts

4 → 96

Calls

4 calls:

933.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
523.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
227.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
143.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify499.0ms (2.4%)

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 → 446

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	10657
1	925	9025
2	3170	8501
3	4767	8501
4	4923	8501

prune611.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	436	10	446
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	440	12	452

Error

0.1b

Counts

452 → 12

Alt Table

Status	Error	Program
	31.1b	(+.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)))))))))))
	22.8b	(-.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))
	31.2b	(+.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)))))
	22.9b	(-.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)))
	23.0b	(-.f64 (.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 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	22.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	23.2b	(/.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)))))
	23.5b	(+.f64 (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 (.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))))))
	40.8b	(+.f64 (fma.f64 1 (/.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)))))
▶	22.8b	(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)))
	27.1b	(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	31.1b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))

Compiler

Compiled 9939 to 3468 computations (65.1% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	3.0b	(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)))

rewrite11.0ms (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:

6.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
1.0ms	(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)))

series890.0ms (4.3%)

Counts

2 → 48

Calls

2 calls:

569.0ms	(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)))
321.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

simplify181.0ms (0.9%)

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 → 168

Iterations

Useful iterations: 2 (0.0ms)

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

prune489.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	314	11	325

Error

0.1b

Counts

325 → 11

Alt Table

Status	Error	Program
	31.1b	(+.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)))))))))))
	22.8b	(-.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))
	31.2b	(+.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)))))
	22.9b	(-.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)))
	23.0b	(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)))))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	22.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	23.2b	(/.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)))))
	23.5b	(+.f64 (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 (.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))))))
▶	22.8b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.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)))))) (neg.f64 (tan.f64 x)))
	27.1b	(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	31.1b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))

Compiler

Compiled 6063 to 2528 computations (58.3% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	3.0b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.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)))))) (neg.f64 (tan.f64 x)))

rewrite37.0ms (0.2%)

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:

16.0ms

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

8.0ms

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

1.0ms

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

series2.2s (10.4%)

Counts

3 → 72

Calls

3 calls:

1.7s

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

260.0ms

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

219.0ms

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

simplify346.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

160 → 299

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	9251
1	886	8844
2	4127	8446
3	5570	8446

prune737.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	454	3	457
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	457	11	468

Error

0.1b

Counts

468 → 11

Alt Table

Status	Error	Program
	31.1b	(+.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)))))))))))
	22.8b	(-.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))
	22.8b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (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)))
	23.5b	(+.f64 (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 (.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))))))
	31.2b	(+.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)))))
	22.9b	(-.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)))
	22.8b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	23.2b	(/.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)))))
	22.8b	(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (/.f64 1 (-.f64 1 (pow.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 eps)) (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)))
	27.1b	(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	31.1b	(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (/.f64 (.f64 (sin.f64 x) (.f64 eps eps)) (cos.f64 x))))

Compiler

Compiled 11718 to 4892 computations (58.3% saved)

regimes6.7s (32.3%)

Accuracy

Total 0.2b remaining (62%)

Threshold costs 0.2b (62%)

Compiler

Compiled 32931 to 17969 computations (45.4% saved)

bsearch89.0ms (0.4%)

Steps

Iters	Range		Point
8	0.00044265271264901963	7.859065038225004	0.00044940075034421095
9	-0.0012175791335672789	-4.764077824079606e-9	-0.00020782601609953486

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	291
1	119	291
2	130	291
3	137	291
4	141	291
5	142	291
6	141	291

end3.0ms (0%)

Compiler: Compiled 186 to 105 computations (43.5% saved)

sample2.8s (13.5%)

Algorithm

1×

intervals

Results

1.1s	3538×	body	1024	valid
655.0ms	1209×	body	2048	valid
263.0ms	1361×	body	512	valid
86.0ms	1292×	body	128	valid
79.0ms	594×	body	256	valid
6.0ms	6×	body	4096	valid

Compiler

Compiled 793 to 438 computations (44.8% 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

analyze2.1s (10.1%)

sample158.0ms (0.8%)

simplify31.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite23.0ms (0.1%)

series270.0ms (1.3%)

simplify218.0ms (1.1%)

prune283.0ms (1.4%)

localize23.0ms (0.1%)

rewrite167.0ms (0.8%)

series1.8s (8.8%)

simplify499.0ms (2.4%)

prune611.0ms (2.9%)

localize23.0ms (0.1%)

rewrite11.0ms (0.1%)

series890.0ms (4.3%)

simplify181.0ms (0.9%)

prune489.0ms (2.4%)

localize43.0ms (0.2%)

rewrite37.0ms (0.2%)

series2.2s (10.4%)

simplify346.0ms (1.7%)

prune737.0ms (3.6%)

regimes6.7s (32.3%)

bsearch89.0ms (0.4%)

simplify11.0ms (0.1%)

end3.0ms (0%)

sample2.8s (13.5%)

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