Details

analyze1.7s (14.6%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.8s (32.5%)

Results

1.9s	3651×	body	1024	valid
1.0s	1221×	body	2048	valid
499.0ms	1413×	body	512	valid
185.0ms	1379×	body	128	valid
142.0ms	590×	body	256	valid
3.0ms	2×	body	4096	valid

Compiler

Compiled 19 to 13 computations (31.6% 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

38.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.4b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	4.3b	(tan.f64 (+.f64 x eps))

series87.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

54.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
33.0ms	(tan.f64 (+.f64 x eps))

rewrite12.0ms (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:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

simplify111.0ms (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

prune104.0ms (0.9%)

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
	32.8b	(+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 x 3)) (pow.f64 (cos.f64 eps) 2)) (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 3)) (.f64 x x) (/.f64 (.f64 (pow.f64 x 3) (pow.f64 (sin.f64 eps) 4)) (pow.f64 (cos.f64 eps) 4)))))
	24.5b	(/.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)))
	29.1b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	24.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	29.4b	(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 1/3 (pow.f64 eps 3))) (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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	29.4b	(+.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 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))

Compiler

Compiled 2989 to 1255 computations (58% saved)

localize13.0ms (0.1%)

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 (tan.f64 x) (tan.f64 eps))
✓	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	2.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series354.0ms (3%)

Counts

4 → 96

Calls

4 calls:

245.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
38.0ms	(*.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))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
67×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
57×	`prod-diff_binary64`
49×	`times-frac_binary64`

Counts

4 → 153

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))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify281.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

223×	`unswap-sqr_binary64`
200×	`distribute-rgt-in_binary64`
194×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`
185×	`associate-l_binary64`

Counts

249 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	9237
1	852	7571
2	2862	7052
3	4563	7052
4	4990	7052
5	4990	7052
6	4882	7052

prune283.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	223	9	232
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	226	12	238

Error

0.1b

Counts

238 → 12

Alt Table

Status	Error	Program
	29.1b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	28.8b	(-.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.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))
	24.4b	(-.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))
	24.4b	(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)))
	24.8b	(-.f64 (/.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 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	25.3b	(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 (tan.f64 x)))
	29.4b	(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 1/3 (pow.f64 eps 3))) (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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
▶	24.4b	(+.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)
	24.5b	(-.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)))
	28.2b	(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)))
	29.4b	(+.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 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	24.4b	(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 (tan.f64 x)))

Compiler

Compiled 8881 to 3032 computations (65.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	2.4b	(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)))

series550.0ms (4.7%)

Counts

2 → 48

Calls

2 calls:

473.0ms

(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)))

76.0ms

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

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
32×	`tan-quot_binary64`
17×	`frac-times_binary64`
17×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`

Counts

2 → 61

Calls

2 calls:

8.0ms

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

1.0ms

(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)))

simplify124.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
744×	`associate-/r*_binary64`
237×	`associate-/r/_binary64`
224×	`associate-r_binary64`
219×	`associate-l_binary64`

Counts

109 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	6615
1	675	6255
2	2414	5516
3	5614	5516

prune349.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	221	11	232

Error

0.1b

Counts

232 → 11

Alt Table

Status	Error	Program
	29.1b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	28.8b	(-.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.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))
	24.4b	(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)))
	24.8b	(-.f64 (/.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 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	25.3b	(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 (tan.f64 x)))
	29.4b	(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 1/3 (pow.f64 eps 3))) (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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	24.5b	(-.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)))
	28.2b	(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)))
▶	24.4b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	29.4b	(+.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 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))
	24.4b	(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 (tan.f64 x)))

Compiler

Compiled 10457 to 4010 computations (61.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (tan.f64 eps)))
✓	0.2b	(.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))
✓	0.2b	(*.f64 (sin.f64 x) (tan.f64 eps))
✓	2.4b	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x)))

series635.0ms (5.4%)

Counts

4 → 96

Calls

4 calls:

540.0ms	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x)))
46.0ms	(.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (tan.f64 eps)))
30.0ms	(*.f64 (sin.f64 x) (tan.f64 eps))
18.0ms	(.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-cbrt-cube_binary64`
23×	`add-exp-log_binary64`
23×	`pow1_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`

Counts

4 → 79

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (sin.f64 x) (tan.f64 eps)))
5.0ms	(.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))
4.0ms	(*.f64 (sin.f64 x) (tan.f64 eps))
1.0ms	(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x)))

simplify186.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-l_binary64`
375×	`associate-r_binary64`
335×	`unswap-sqr_binary64`
236×	`cancel-sign-sub-inv_binary64`
186×	`*-commutative_binary64`

Counts

175 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	357	7712
1	950	7092
2	3610	7076
3	4905	7072
4	4965	7072

prune280.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	173	12	185

Error

0.1b

Counts

185 → 12

Alt Table

Status	Error	Program
	29.1b	(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	28.8b	(-.f64 (/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.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))
	24.4b	(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)))
	24.8b	(-.f64 (/.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 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	25.3b	(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 (tan.f64 x)))
	29.4b	(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (.f64 1/3 (pow.f64 eps 3))) (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 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	24.5b	(-.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)))
	24.4b	(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 (tan.f64 x)))
	25.1b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x)))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))))) (cbrt.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))))) 0)
	28.2b	(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)))
✓	24.4b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (tan.f64 eps))) (.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
	29.4b	(+.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 1/3 (pow.f64 eps 3)) (.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))))))

Compiler

Compiled 9622 to 3524 computations (63.4% saved)

regimes2.2s (18.8%)

Accuracy

Total 0.2b remaining (61%)

Threshold costs 0.2b (61%)

Counts

285 → 3

Compiler

Compiled 26748 to 14762 computations (44.8% saved)

bsearch105.0ms (0.9%)

Steps

Iters	Range		Point
10	8.28463773366438e-17	0.00014690515572541568	5.9543033066741405e-5
8	-0.0006637061522229891	-3.3852055228738227e-7	-2.3680288234376444e-5

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
14×	`*-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	209
1	82	209
2	95	209
3	107	209
4	121	209
5	129	209
6	134	209
7	136	209
8	135	209

end356.0ms (3%)

Compiler: Compiled 839 to 429 computations (48.9% 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	60	209
1	82	209
2	95	209
3	107	209
4	121	209
5	129	209
6	134	209
7	136	209
8	135	209

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	60	209
1	82	209
2	95	209
3	107	209
4	121	209
5	129	209
6	134	209
7	136	209
8	135	209

Details

analyze1.7s (14.6%)

sample3.8s (32.5%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series87.0ms (0.7%)

rewrite12.0ms (0.1%)

simplify111.0ms (1%)

prune104.0ms (0.9%)

localize13.0ms (0.1%)

series354.0ms (3%)

rewrite39.0ms (0.3%)

simplify281.0ms (2.4%)

prune283.0ms (2.4%)

localize15.0ms (0.1%)

series550.0ms (4.7%)

rewrite15.0ms (0.1%)

simplify124.0ms (1.1%)

prune349.0ms (3%)

localize25.0ms (0.2%)

series635.0ms (5.4%)

rewrite22.0ms (0.2%)

simplify186.0ms (1.6%)

prune280.0ms (2.4%)

regimes2.2s (18.8%)

bsearch105.0ms (0.9%)

simplify11.0ms (0.1%)

end356.0ms (3%)

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

Iter	Nodes	Cost
0	60	209
1	82	209
2	95	209
3	107	209
4	121	209
5	129	209
6	134	209
7	136	209
8	135	209