Details

analyze786.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
43.7%	56.2%	0%	6
46.9%	53.1%	0%	7
48.4%	51.5%	0%	8
48.4%	51.5%	0%	9
48.4%	51.5%	0%	10
48.4%	51.5%	0%	11
48.5%	51.4%	0%	12
48.6%	51.4%	0%	13
48.6%	51.3%	0%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample1.8s (17.3%)

Results

811.0ms	2101×	body	1024	valid
499.0ms	4544×	body	128	valid
310.0ms	1070×	body	512	valid
111.0ms	533×	body	256	valid
4.0ms	8×	body	2048	valid

Compiler

Compiled 33 to 17 computations (48.5% saved)

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

678×	`unsub-neg_binary64`
627×	`times-frac_binary64`
565×	`div-sub_binary64`
547×	`fma-def_binary64`
526×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	19	22
2	30	22
3	47	22
4	94	22
5	137	22
6	211	22
7	437	22
8	928	22
9	1718	22
10	3074	22
11	3861	22
12	4442	22
13	4822	22

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.3b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 92 to 45 computations (51.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series128.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

90.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
17.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
11.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
11×	`pow1_binary64`

Counts

4 → 102

Calls

4 calls:

4.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
2.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Rules

588×	`cancel-sign-sub-inv_binary64`
342×	`fma-def_binary64`
323×	`fma-neg_binary64`
287×	`associate-l_binary64`
237×	`associate-r_binary64`

Counts

150 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3084
1	360	2781
2	960	2730
3	3123	2721
4	5035	2721

prune237.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	146	13	159
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	13	161

Error

0.0b

Counts

161 → 13

Alt Table

Status	Error	Program
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.3b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(/.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.7b	(/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	1.9b	(/.f64 (log.f64 (/.f64 (exp.f64 1) (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))))
	0.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
▶	0.3b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))

Compiler

Compiled 4070 to 1943 computations (52.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
✓	0.3b	(log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))

series1.9s (18.1%)

Counts

2 → 24

Calls

2 calls:

1.8s

(log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))

107.0ms

(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms

(log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))

simplify138.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

497×	`associate-l_binary64`
460×	`associate-r_binary64`
453×	`fma-def_binary64`
373×	`cancel-sign-sub-inv_binary64`
233×	`times-frac_binary64`

Counts

46 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	69	1518
1	152	1248
2	361	1244
3	1065	1242
4	4440	1242
5	4668	1114
6	4961	1114
7	5000	1114
8	4873	1114

prune291.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	153	12	165

Error

0.0b

Counts

165 → 12

Alt Table

Status	Error	Program
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶	0.3b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(/.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.7b	(/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(expm1.f64 (log.f64 (+.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	1.9b	(/.f64 (log.f64 (/.f64 (exp.f64 1) (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))

Compiler

Compiled 4090 to 2154 computations (47.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))
✓	0.2b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))))
✓	0.5b	(pow.f64 (tan.f64 x) 4)
✓	0.6b	(pow.f64 (tan.f64 x) 6)

series324.0ms (3%)

Counts

4 → 48

Calls

4 calls:

241.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))))
36.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))
26.0ms	(pow.f64 (tan.f64 x) 6)
20.0ms	(pow.f64 (tan.f64 x) 4)

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`difference-of-squares_binary64`
24×	`add-cube-cbrt_binary64`

Counts

4 → 121

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))))
3.0ms	(pow.f64 (tan.f64 x) 4)
2.0ms	(pow.f64 (tan.f64 x) 6)
0.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4))

simplify156.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-l_binary64`
487×	`fma-def_binary64`
471×	`associate-r_binary64`
251×	`associate-/l*_binary64`
214×	`distribute-rgt-in_binary64`

Counts

169 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	5070
1	501	4763
2	1248	4749
3	4979	4749
4	4974	4749

prune460.0ms (4.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	195	13	208

Error

0.0b

Counts

208 → 13

Alt Table

Status	Error	Program
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 6)) (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (cbrt.f64 (pow.f64 (tan.f64 x) 6)))) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	1.6b	(/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.7b	(/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(expm1.f64 (log.f64 (+.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	0.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.6b	(/.f64 (/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (cos.f64 x) 6))) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(/.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
▶	0.4b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))

Compiler

Compiled 7718 to 4546 computations (41.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))
	0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
✓	0.3b	(log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))))

series2.0s (18.7%)

Counts

3 → 36

Calls

3 calls:

1.8s

(log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))))

97.0ms

(/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))

93.0ms

(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`times-frac_binary64`
73×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
61×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`

Counts

3 → 132

Calls

3 calls:

7.0ms

(/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))

0.0ms

(log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))

simplify186.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-neg_binary64`
459×	`distribute-rgt-in_binary64`
425×	`cancel-sign-sub-inv_binary64`
242×	`fma-def_binary64`
207×	`times-frac_binary64`

Counts

168 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	6383
1	351	5442
2	941	5303
3	2575	5303
4	4788	5303
5	5356	5303

prune477.0ms (4.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	238	13	251

Error

0.0b

Counts

251 → 13

Alt Table

Status	Error	Program
	0.4b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(/.f64 (/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 6)) (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (cbrt.f64 (pow.f64 (tan.f64 x) 6)))) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	1.6b	(/.f64 (log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 6)) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (.f64 (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.7b	(/.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (.f64 (tan.f64 x) (tan.f64 x)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(expm1.f64 (log.f64 (+.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	0.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(-.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.6b	(/.f64 (/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 6) (pow.f64 (cos.f64 x) 6))) (+.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) (pow.f64 (tan.f64 x) 4)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(/.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
✓	0.4b	(expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))))

Compiler

Compiled 7404 to 4117 computations (44.4% saved)

regimes1.2s (11%)

Accuracy

Total 0.3b remaining (78.9%)

Threshold costs 0.3b (78.9%)

Counts

256 → 1

Compiler

Compiled 24734 to 15094 computations (39% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	13	22
2	15	22
3	16	22
4	15	22

end233.0ms (2.2%)

Compiler: Compiled 388 to 218 computations (43.8% saved)

Details

analyze786.0ms (7.4%)

sample1.8s (17.3%)

simplify94.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series128.0ms (1.2%)

rewrite16.0ms (0.1%)

simplify103.0ms (1%)

prune237.0ms (2.2%)

localize10.0ms (0.1%)

series1.9s (18.1%)

rewrite2.0ms (0%)

simplify138.0ms (1.3%)

prune291.0ms (2.7%)

localize12.0ms (0.1%)

series324.0ms (3%)

rewrite24.0ms (0.2%)

simplify156.0ms (1.5%)

prune460.0ms (4.3%)

localize13.0ms (0.1%)

series2.0s (18.7%)

rewrite23.0ms (0.2%)

simplify186.0ms (1.7%)

prune477.0ms (4.5%)

regimes1.2s (11%)

simplify2.0ms (0%)

end233.0ms (2.2%)

Profiling