Details

analyze793.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample2.4s (25.9%)

Results

1.1s	2121×	body	1024	valid
674.0ms	4587×	body	128	valid
395.0ms	1046×	body	512	valid
132.0ms	498×	body	256	valid
3.0ms	4×	body	2048	valid

Compiler

Compiled 50 to 26 computations (48% saved)

simplify132.0ms (1.4%)

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

prune6.0ms (0.1%)

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)

localize13.0ms (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))

series241.0ms (2.6%)

Counts

4 → 48

Calls

4 calls:

161.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
35.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)
24.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
21.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite32.0ms (0.3%)

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:

8.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
1.0ms	(fma.f64 (tan.f64 x) (tan.f64 x) 1)

simplify177.0ms (1.9%)

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

prune249.0ms (2.6%)

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
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	13.8b	(.f64 (sqrt.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x)))) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	1.0b	(/.f64 (-.f64 1 (*.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 5) (cbrt.f64 (tan.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))))
	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))))
	1.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (log1p.f64 (expm1.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))))
	0.4b	(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	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (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)))
▶	0.3b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.5b	(*.f64 (/.f64 (+.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))) (/.f64 (-.f64 1 (tan.f64 x)) (hypot.f64 1 (tan.f64 x))))
	0.8b	(.f64 (/.f64 (+.f64 1 (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)))) (/.f64 (-.f64 1 (tan.f64 x)) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))

Compiler

Compiled 3964 to 1913 computations (51.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series175.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

110.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
37.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
18.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))
9.0ms	(*.f64 (sin.f64 x) (tan.f64 x))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
50×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
33×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
9.0ms	(*.f64 (sin.f64 x) (tan.f64 x))
8.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))
6.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))

simplify177.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

631×	`fma-def_binary64`
328×	`associate-/r/_binary64`
242×	`cancel-sign-sub-inv_binary64`
210×	`distribute-rgt-neg-in_binary64`
202×	`exp-prod_binary64`

Counts

184 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	5019
1	570	4557
2	2019	4173
3	4435	4173
4	4896	4173

prune467.0ms (5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	186	10	196
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	193	16	209

Error

0.0b

Counts

209 → 16

Alt Table

Status	Error	Program
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 (-.f64 1 (/.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 x) (tan.f64 x)))) (cos.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 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(/.f64 (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (cos.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	(/.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))))
	13.7b	(/.f64 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (sqrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))))))
	1.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (log1p.f64 (expm1.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))))
	0.3b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(/.f64 1 (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))))) (/.f64 (cbrt.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.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)))) (/.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	13.8b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(/.f64 (-.f64 (.f64 1 1) (.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (sin.f64 x) (/.f64 (tan.f64 x) (cos.f64 x)) 1)))

Compiler

Compiled 6752 to 2538 computations (62.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series167.0ms (1.8%)

Counts

2 → 24

Calls

2 calls:

92.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
75.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 77

Calls

2 calls:

10.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
2.0ms	(/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))

simplify108.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-neg_binary64`
627×	`distribute-rgt-in_binary64`
383×	`cancel-sign-sub-inv_binary64`
244×	`associate-l_binary64`
234×	`fma-def_binary64`

Counts

101 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	280	2128
2	767	2112
3	2212	2112
4	4886	2112
5	5267	2112

prune487.0ms (5.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	201	13	214

Error

0.0b

Counts

214 → 13

Alt Table

Status	Error	Program
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(.f64 (+.f64 1 (tan.f64 x)) (.f64 (-.f64 1 (tan.f64 x)) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))
	0.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.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)))) (/.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	1.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (log1p.f64 (expm1.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))))
▶	0.3b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.3b	(.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (exp.f64 (neg.f64 (log1p.f64 (*.f64 (tan.f64 x) (tan.f64 x))))))
	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)))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))))) (/.f64 (cbrt.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	13.8b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(/.f64 (-.f64 (.f64 1 1) (.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)) (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (*.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (fma.f64 (sin.f64 x) (/.f64 (tan.f64 x) (cos.f64 x)) 1)))

Compiler

Compiled 5406 to 2752 computations (49.1% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (tan.f64 x) (cos.f64 x))
✓	0.2b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
✓	0.2b	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
✓	45.1b	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))

series416.0ms (4.4%)

Counts

4 → 48

Calls

4 calls:

256.0ms	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
94.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))
33.0ms	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
33.0ms	(/.f64 (tan.f64 x) (cos.f64 x))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`

Counts

4 → 131

Calls

4 calls:

16.0ms	(*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))
8.0ms	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
8.0ms	(/.f64 (tan.f64 x) (cos.f64 x))
1.0ms	(fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))

simplify303.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
483×	`associate-/l*_binary64`
400×	`times-frac_binary64`
325×	`associate-*l/_binary64`
272×	`distribute-rgt-in_binary64`

Counts

179 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	5524
1	526	4396
2	1481	3399
3	4095	3397
4	4968	3397
5	4824	3397

prune1.2s (12.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	407	5	412
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	414	11	425

Error

Counts

425 → 11

Alt Table

Status	Error	Program
	1.6b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (*.f64 (tan.f64 x) (tan.f64 x))))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.4b	(.f64 (+.f64 1 (tan.f64 x)) (.f64 (-.f64 1 (tan.f64 x)) (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.5b	(cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))) (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))) (.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))))
	2.6b	(/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (log1p.f64 (expm1.f64 (/.f64 (tan.f64 x) (cos.f64 x))))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))
	0.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (cbrt.f64 (/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (cbrt.f64 (/.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (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)))
	0.7b	(/.f64 (.f64 (cbrt.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1))))) (cbrt.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))))) (/.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1) (cbrt.f64 (+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))) (fma.f64 (neg.f64 (/.f64 (tan.f64 x) (cos.f64 x))) (/.f64 (sin.f64 x) 1) (*.f64 (/.f64 (tan.f64 x) (cos.f64 x)) (/.f64 (sin.f64 x) 1)))))))
	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (exp.f64 (neg.f64 (log1p.f64 (*.f64 (tan.f64 x) (tan.f64 x))))))
	0.7b	(.f64 (.f64 (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (cbrt.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))))) (/.f64 (cbrt.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1)))
	0.4b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (*.f64 (sin.f64 x) (/.f64 (tan.f64 x) (cos.f64 x)))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))))
	0.4b	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))))

Compiler

Compiled 21344 to 8519 computations (60.1% saved)

regimes1.4s (14.6%)

Accuracy

Total 0.3b remaining (77.1%)

Threshold costs 0.3b (77.1%)

Counts

287 → 1

Compiler

Compiled 35581 to 19653 computations (44.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	17	22
2	23	22
3	27	22
4	29	22
5	28	22

end258.0ms (2.7%)

Compiler: Compiled 622 to 306 computations (50.8% saved)

Details

analyze793.0ms (8.4%)

sample2.4s (25.9%)

simplify132.0ms (1.4%)

prune6.0ms (0.1%)

localize13.0ms (0.1%)

series241.0ms (2.6%)

rewrite32.0ms (0.3%)

simplify177.0ms (1.9%)

prune249.0ms (2.6%)

localize15.0ms (0.2%)

series175.0ms (1.9%)

rewrite48.0ms (0.5%)

simplify177.0ms (1.9%)

prune467.0ms (5%)

localize10.0ms (0.1%)

series167.0ms (1.8%)

rewrite18.0ms (0.2%)

simplify108.0ms (1.1%)

prune487.0ms (5.2%)

localize33.0ms (0.3%)

series416.0ms (4.4%)

rewrite53.0ms (0.6%)

simplify303.0ms (3.2%)

prune1.2s (12.9%)

regimes1.4s (14.6%)

simplify3.0ms (0%)

end258.0ms (2.7%)

Profiling