Details

analyze1.2s (10.7%)

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)

sample3.8s (33%)

Results

1.8s	3620×	body	1024	valid
1.0s	1247×	body	2048	valid
569.0ms	1454×	body	512	valid
199.0ms	1296×	body	128	valid
147.0ms	634×	body	256	valid
7.0ms	5×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify10.0ms (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

34.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.6b	(-.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
✓	1.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	3.5b	(tan.f64 (+.f64 x eps))

series69.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

44.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
25.0ms	(tan.f64 (+.f64 x eps))

rewrite10.0ms (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))

simplify113.0ms (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

prune92.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	5	94

Error

0.2b

Counts

94 → 5

Alt Table

Status	Error	Program
	33.6b	(+.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)))))
	33.2b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	19.6b	(/.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)))))
	19.6b	(/.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)))
▶	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

Compiler

Compiled 2705 to 1073 computations (60.3% saved)

localize9.0ms (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))
✓	2.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series353.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

254.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
39.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
33.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
27.0ms	(+.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:

11.0ms	(-.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))
3.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify285.0ms (2.5%)

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

prune275.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	220	12	232
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	223	14	237

Error

0.1b

Counts

237 → 14

Alt Table

Status	Error	Program
	20.5b	(-.f64 (/.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	33.6b	(+.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)))))
	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (/.f64 (exp.f64 1) (exp.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	33.2b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	19.4b	(+.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)
	19.5b	(-.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))
	21.2b	(/.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)))
	19.7b	(-.f64 (/.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (cos.f64 x) (cos.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	21.0b	(log1p.f64 (expm1.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
	19.8b	(/.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)))))
	42.7b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.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))))))
▶	19.4b	(-.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))
	19.6b	(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)))
	40.6b	(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.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))))))

Compiler

Compiled 8991 to 3024 computations (66.4% 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 eps) (tan.f64 x))
✓	2.7b	(-.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))
✓	52.0b	(fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) (*.f64 (tan.f64 eps) (tan.f64 x)))

series463.0ms (4%)

Counts

3 → 72

Calls

3 calls:

321.0ms

(-.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))

108.0ms

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

33.0ms

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

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
66×	`prod-diff_binary64`
65×	`times-frac_binary64`
64×	`add-cube-cbrt_binary64`

Counts

3 → 141

Calls

3 calls:

12.0ms

(-.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))

4.0ms

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

0.0ms

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

simplify176.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

815×	`associate-/l*_binary64`
223×	`distribute-rgt-in_binary64`
202×	`distribute-lft-in_binary64`
180×	`unswap-sqr_binary64`
179×	`associate-/r/_binary64`

Counts

213 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	13234
1	752	8227
2	2523	6061
3	5014	6061

prune401.0ms (3.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	259	13	272

Error

0.1b

Counts

272 → 13

Alt Table

Status	Error	Program
	20.5b	(-.f64 (/.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	33.6b	(+.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)))))
	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (/.f64 (exp.f64 1) (exp.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	33.2b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
▶	19.4b	(+.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)
	19.5b	(-.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))
	21.2b	(/.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)))
	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 (fma.f64 1 1 (neg.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) (*.f64 (tan.f64 eps) (tan.f64 x))))) (tan.f64 x))
	20.9b	(log1p.f64 (expm1.f64 (-.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))))
	19.8b	(/.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)))))
	19.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (+.f64 0 (pow.f64 (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x))) 3))) (.f64 (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (tan.f64 x))) 0)
	19.6b	(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)))
	41.6b	(+.f64 (fma.f64 1 (/.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))))) (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)))))

Compiler

Compiled 13639 to 3837 computations (71.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (tan.f64 x) (tan.f64 eps) 1)
	0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
✓	2.7b	(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)))

series474.0ms (4.1%)

Counts

3 → 72

Calls

3 calls:

381.0ms

(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)))

61.0ms

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

32.0ms

(fma.f64 (tan.f64 x) (tan.f64 eps) 1)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`tan-quot_binary64`
4×	`*-un-lft-identity_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms

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

0.0ms

(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)))

0.0ms

(fma.f64 (tan.f64 x) (tan.f64 eps) 1)

simplify147.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
377×	`unswap-sqr_binary64`
279×	`times-frac_binary64`
205×	`associate-/l*_binary64`
200×	`associate-r_binary64`

Counts

119 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	8176
1	726	7885
2	3246	7756
3	5086	7756

prune344.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	190	13	203

Error

0.0b

Counts

203 → 13

Alt Table

Status	Error	Program
	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (/.f64 (exp.f64 1) (exp.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
	33.2b	(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
	19.5b	(-.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))
	21.2b	(/.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)))
	19.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 (fma.f64 1 1 (neg.f64 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (fma.f64 (neg.f64 (tan.f64 eps)) (tan.f64 x) (*.f64 (tan.f64 eps) (tan.f64 x))))) (tan.f64 x))
	28.4b	(+.f64 (log.f64 (exp.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)
	19.5b	(+.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 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
	19.8b	(/.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)))))
	33.6b	(+.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)))))
	20.9b	(log1p.f64 (expm1.f64 (-.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))))
	19.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 eps) (tan.f64 x)) (+.f64 0 (pow.f64 (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x))) 3))) (.f64 (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 eps) (tan.f64 x)))) (neg.f64 (tan.f64 x))) 0)
	19.6b	(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)))
	19.5b	(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (pow.f64 (.f64 (sin.f64 x) (tan.f64 eps)) 3) (pow.f64 (cos.f64 x) 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)

Compiler

Compiled 9445 to 3923 computations (58.5% saved)

regimes2.7s (23%)

Accuracy

Total 0.4b remaining (71.9%)

Threshold costs 0.4b (71.9%)

Counts

286 → 3

Compiler

Compiled 27315 to 14198 computations (48% saved)

bsearch93.0ms (0.8%)

Steps

Iters	Range		Point
5	5.376960049285448e-22	1.1697437921212775e-21	1.155034655722551e-21
10	-637.2420183996632	-1.394585200786095e-16	-3.3419396080878345e-7

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	181
1	74	181
2	87	181
3	94	181
4	97	181
5	98	181
6	97	181

end395.0ms (3.4%)

Compiler: Compiled 688 to 366 computations (46.8% 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

analyze1.2s (10.7%)

sample3.8s (33%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series69.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify113.0ms (1%)

prune92.0ms (0.8%)

localize9.0ms (0.1%)

series353.0ms (3.1%)

rewrite39.0ms (0.3%)

simplify285.0ms (2.5%)

prune275.0ms (2.4%)

localize15.0ms (0.1%)

series463.0ms (4%)

rewrite43.0ms (0.4%)

simplify176.0ms (1.5%)

prune401.0ms (3.5%)

localize17.0ms (0.2%)

series474.0ms (4.1%)

rewrite6.0ms (0.1%)

simplify147.0ms (1.3%)

prune344.0ms (3%)

regimes2.7s (23%)

bsearch93.0ms (0.8%)

simplify8.0ms (0.1%)

end395.0ms (3.4%)

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