Details

analyze1.7s (5.4%)

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)

sample4.9s (15.6%)

Results

2.5s	3586×	body	1024	valid
1.3s	1276×	body	2048	valid
640.0ms	1483×	body	512	valid
254.0ms	601×	body	256	valid
212.0ms	1310×	body	128	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (0%)

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

35.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.9b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.2b	(tan.f64 (+.f64 x eps))

series77.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
30.0ms	(tan.f64 (+.f64 x eps))

rewrite12.0ms (0%)

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))
4.0ms	(tan.f64 (+.f64 x eps))

simplify108.0ms (0.3%)

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

prune105.0ms (0.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Error

0.2b

Counts

94 → 6

Alt Table

Status	Error	Program
	20.7b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	20.8b	(/.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)))
	34.1b	(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
▶	20.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	33.5b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	34.3b	(+.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)))))

Compiler

Compiled 2915 to 1203 computations (58.7% saved)

localize10.0ms (0%)

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))
✓	2.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series607.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

271.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
236.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
50.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
49.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

rewrite128.0ms (0.4%)

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:

26.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
19.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
7.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify480.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

228×	`unswap-sqr_binary64`
225×	`associate-+r+_binary64`
225×	`distribute-rgt-in_binary64`
203×	`distribute-lft-in_binary64`
184×	`associate-l_binary64`

Counts

267 → 245

Iterations

Useful iterations: 2 (0.0ms)

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

prune584.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	232	13	245
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	235	16	251

Error

0.1b

Counts

251 → 16

Alt Table

Status	Error	Program
	53.0b	(.f64 (+.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (tan.f64 x))) (-.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (tan.f64 x))))
	24.3b	(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)))
	20.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (tan.f64 x))
	20.7b	(fma.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))))) (neg.f64 (tan.f64 x)))
	33.5b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	44.1b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 1) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
▶	20.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
	34.3b	(+.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)))))
	21.6b	(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)))
	21.0b	(+.f64 (fma.f64 1 (/.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))))))
	23.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) (-.f64 (.f64 (tan.f64 eps) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	34.1b	(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	20.6b	(+.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)
	21.3b	(+.f64 (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 (.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))))))
	40.0b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x))))
	25.3b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 10009 to 3456 computations (65.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (tan.f64 x))
✓	0.3b	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
✓	2.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
✓	3.4b	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))

series9.2s (29.1%)

Counts

4 → 84

Calls

4 calls:

5.5s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
2.6s	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
966.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
14.0ms	(exp.f64 (tan.f64 x))

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

183×	`*-un-lft-identity_binary64`
138×	`add-sqr-sqrt_binary64`
97×	`times-frac_binary64`
90×	`prod-diff_binary64`
85×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

23.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
5.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
3.0ms	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
3.0ms	(exp.f64 (tan.f64 x))

simplify515.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

255×	`associate-/r/_binary64`
224×	`unswap-sqr_binary64`
160×	`associate-+r+_binary64`
156×	`+-commutative_binary64`
154×	`associate-r_binary64`

Counts

279 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	10716
1	888	8677
2	2943	8377
3	4992	8377
4	4929	8377

prune616.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	248	6	254
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	257	13	270

Error

0.1b

Counts

270 → 13

Alt Table

Status	Error	Program
	20.7b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	23.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) (-.f64 (.f64 (tan.f64 eps) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	20.8b	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (sin.f64 x))) (*.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (cos.f64 x)))
	44.1b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 1) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	34.1b	(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	34.2b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (fma.f64 1/3 (pow.f64 eps 3) (.f64 4/3 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (pow.f64 eps 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))))
	24.3b	(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)))
▶	20.6b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	20.6b	(+.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)
	40.0b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x))))
	34.2b	(+.f64 (.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (.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))))
	21.0b	(+.f64 (fma.f64 1 (/.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))))))
	25.3b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 10836 to 3453 computations (68.1% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(exp.f64 (tan.f64 x))
	0.3b	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
✓	2.1b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	3.4b	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))

series5.5s (17.5%)

Counts

1 → 24

Calls

1 calls:

5.5s

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

2.0ms

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

simplify181.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

839×	`associate-/l*_binary64`
640×	`fma-def_binary64`
506×	`associate-/r*_binary64`
147×	`associate-/r/_binary64`
136×	`unswap-sqr_binary64`

Counts

34 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	4906
1	419	4559
2	1558	3874
3	4980	3874

prune1.4s (4.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	366	1	367
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	366	14	380

Error

0.0b

Counts

380 → 14

Alt Table

Status	Error	Program
	20.7b	(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (neg.f64 (tan.f64 x)))
	23.0b	(-.f64 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) (-.f64 (.f64 (tan.f64 eps) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	20.8b	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (sin.f64 x))) (*.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (cos.f64 x)))
	44.1b	(fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) 1) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
	34.1b	(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
	34.2b	(+.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (fma.f64 1/3 (pow.f64 eps 3) (.f64 4/3 (.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (pow.f64 eps 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))))
	24.3b	(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)))
✓	20.6b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	20.6b	(+.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)
	21.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x))))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (.f64 1 1) (.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))) (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))))) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))))
	40.0b	(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x))))
	34.2b	(+.f64 (.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (.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))))
	21.0b	(+.f64 (fma.f64 1 (/.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))))))
	25.3b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))

Compiler

Compiled 18267 to 5654 computations (69% saved)

regimes4.4s (14.1%)

Accuracy

Total 0.2b remaining (63.5%)

Threshold costs 0.2b (63.5%)

Counts

294 → 3

Compiler

Compiled 26745 to 14189 computations (46.9% saved)

bsearch138.0ms (0.4%)

Steps

Iters	Range		Point
11	5.117691114295571e-21	12798436.935330635	6.61700448350665e-5
9	-0.036312549220129324	-1.4686995083758297e-7	-3.231461580256822e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
11×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	195
1	84	195
2	100	195
3	109	195
4	114	195
5	115	195
6	114	195

end568.0ms (1.8%)

Compiler: Compiled 889 to 448 computations (49.6% 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

analyze1.7s (5.4%)

sample4.9s (15.6%)

simplify11.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0%)

series77.0ms (0.2%)

rewrite12.0ms (0%)

simplify108.0ms (0.3%)

prune105.0ms (0.3%)

localize10.0ms (0%)

series607.0ms (1.9%)

rewrite128.0ms (0.4%)

simplify480.0ms (1.5%)

prune584.0ms (1.9%)

localize25.0ms (0.1%)

series9.2s (29.1%)

rewrite82.0ms (0.3%)

simplify515.0ms (1.6%)

prune616.0ms (2%)

localize39.0ms (0.1%)

series5.5s (17.5%)

rewrite3.0ms (0%)

simplify181.0ms (0.6%)

prune1.4s (4.6%)

regimes4.4s (14.1%)

bsearch138.0ms (0.4%)

simplify11.0ms (0%)

end568.0ms (1.8%)

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