Details

analyze1.7s (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)

sample157.0ms (0.9%)

Algorithm

1×

intervals

Results

81.0ms	119×	body	1024	valid
32.0ms	33×	body	2048	valid
17.0ms	46×	body	512	valid
5.0ms	40×	body	128	valid
4.0ms	17×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify21.0ms (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

36.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.8b	(tan.f64 (+.f64 x eps))

series163.0ms (1%)

Counts

2 → 48

Calls

2 calls:

102.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
61.0ms	(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))

simplify186.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
909×	`times-frac_binary64`
194×	`associate-+r+_binary64`
142×	`unswap-sqr_binary64`
125×	`+-commutative_binary64`

Counts

91 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2570
1	507	2289
2	1787	2148
3	4965	2145
4	4986	2145
5	4943	2145

prune339.0ms (2%)

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
	33.0b	(+.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)))))
▶	21.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	21.1b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	21.1b	(/.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)))
	33.0b	(+.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)))))))))))
	32.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 3071 to 1307 computations (57.4% saved)

localize24.0ms (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))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series971.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

577.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
250.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
77.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
66.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite130.0ms (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:

64.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
13.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
12.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify407.0ms (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 → 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

prune459.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	238	7	245
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	241	10	251

Error

0.1b

Counts

251 → 10

Alt Table

Status	Error	Program
▶	21.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
	21.0b	(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)))
	21.1b	(-.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)))
	23.9b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) 3))
	21.0b	(-.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))
	21.2b	(/.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)))))
	33.0b	(+.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)))))))))))
	22.0b	(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
	32.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	33.0b	(+.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 9571 to 3332 computations (65.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
✓	0.2b	(*.f64 (tan.f64 x) (sin.f64 eps))
✓	2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))

series498.0ms (2.9%)

Counts

3 → 72

Calls

3 calls:

318.0ms

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

153.0ms

(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))

27.0ms

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

rewrite135.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`*-un-lft-identity_binary64`
137×	`add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
90×	`prod-diff_binary64`
82×	`add-cube-cbrt_binary64`

Counts

3 → 185

Calls

3 calls:

42.0ms

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

9.0ms

(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))

8.0ms

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

simplify457.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

232×	`unswap-sqr_binary64`
204×	`associate-/l*_binary64`
167×	`associate-l_binary64`
162×	`associate-r_binary64`
146×	`cancel-sign-sub-inv_binary64`

Counts

257 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	381	12527
1	881	9754
2	3117	8984
3	4658	8984
4	4922	8984

prune362.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	274	2	276
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	277	9	286

Error

0.1b

Counts

286 → 9

Alt Table

Status	Error	Program
	21.1b	(-.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)))
	23.9b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)) 3))
	33.0b	(+.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)))))
	21.2b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))))
	21.0b	(-.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))
▶	21.0b	(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)))
	21.9b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (neg.f64 (tan.f64 x)))
	33.0b	(+.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)))))))))))
	32.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 11668 to 3518 computations (69.8% saved)

localize13.0ms (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))
	0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.5b	(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)))

series271.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

178.0ms	(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)))
93.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

rewrite7.0ms (0%)

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:

4.0ms	(/.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)))

simplify87.0ms (0.5%)

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 → 91

Iterations

Useful iterations: 2 (0.0ms)

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

prune220.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	168	9	177

Error

0.1b

Counts

177 → 9

Alt Table

Status	Error	Program
	33.0b	(+.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)))))
	21.2b	(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (sin.f64 x) (+.f64 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)) -1))) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))))
	21.3b	(fma.f64 (fma.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
	21.0b	(-.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))
✓	21.0b	(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)))
	21.9b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (neg.f64 (tan.f64 x)))
	21.1b	(-.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)))
	33.0b	(+.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)))))))))))
	32.6b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))

Compiler

Compiled 5375 to 2155 computations (59.9% saved)

regimes5.1s (30.1%)

Accuracy

Total 0.2b remaining (56.8%)

Threshold costs 0.2b (56.8%)

Counts

357 → 3

Compiler

Compiled 31632 to 17756 computations (43.9% saved)

bsearch188.0ms (1.1%)

Steps

Iters	Range		Point
8	1.3592012631939926e-8	8.352656877259924e-5	3.118191246439813e-7
6	-2.0553997951368072e-8	-1.7190570600130333e-9	-2.01426406875669e-8

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	125
1	64	125
2	86	125
3	101	125
4	110	125
5	113	125
6	111	125

end2.0ms (0%)

Compiler: Compiled 81 to 46 computations (43.2% saved)

sample4.9s (29.2%)

Algorithm

1×

intervals

Results

2.0s	3464×	body	1024	valid
1.3s	1207×	body	2048	valid
502.0ms	1414×	body	512	valid
142.0ms	599×	body	256	valid
141.0ms	1314×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 519 to 302 computations (41.8% 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

analyze1.7s (10.1%)

sample157.0ms (0.9%)

simplify21.0ms (0.1%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series163.0ms (1%)

rewrite23.0ms (0.1%)

simplify186.0ms (1.1%)

prune339.0ms (2%)

localize24.0ms (0.1%)

series971.0ms (5.7%)

rewrite130.0ms (0.8%)

simplify407.0ms (2.4%)

prune459.0ms (2.7%)

localize26.0ms (0.2%)

series498.0ms (2.9%)

rewrite135.0ms (0.8%)

simplify457.0ms (2.7%)

prune362.0ms (2.1%)

localize13.0ms (0.1%)

series271.0ms (1.6%)

rewrite7.0ms (0%)

simplify87.0ms (0.5%)

prune220.0ms (1.3%)

regimes5.1s (30.1%)

bsearch188.0ms (1.1%)

simplify11.0ms (0.1%)

end2.0ms (0%)

sample4.9s (29.2%)

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