Details

analyze1.1s (13.2%)

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
18.7%	81.2%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.6%	52.3%	0.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample79.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	32×	body	2048	valid
20.0ms	38×	body	1024	valid
13.0ms	142×	body	128	valid
7.0ms	25×	body	512	valid
4.0ms	18×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	12	20
2	14	20
3	14	20

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

36.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	36.1b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 x (*.f64 y 2))
✓	7.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	28.0b	(tan.f64 (/.f64 x (*.f64 y 2)))
✓	28.2b	(sin.f64 (/.f64 x (*.f64 y 2)))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 72

Calls

4 calls:

27.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
3.0ms	(/.f64 x (*.f64 y 2))
1.0ms	(sin.f64 (/.f64 x (*.f64 y 2)))
1.0ms	(tan.f64 (/.f64 x (*.f64 y 2)))

series151.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
34.0ms	(tan.f64 (/.f64 x (*.f64 y 2)))
23.0ms	(/.f64 x (*.f64 y 2))
7.0ms	(sin.f64 (/.f64 x (*.f64 y 2)))

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

751×	`times-frac_binary64`
477×	`associate-/l*_binary64`
353×	`associate-/r*_binary64`
284×	`unswap-sqr_binary64`
222×	`fma-neg_binary64`

Counts

168 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	3106
1	372	2919
2	1004	2853
3	4130	2826
4	4953	2826

prune151.0ms (1.9%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	193	23	216
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	23	217

Error

25.2b

Counts

217 → 23

Alt Table

Status	Error	Program
	59.9b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (log.f64 (exp.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	36.8b	(/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.2b	(/.f64 (log.f64 (exp.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	57.7b	(/.f64 (tan.f64 (exp.f64 (-.f64 (log.f64 x) (log.f64 (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	37.0b	(/.f64 (tan.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 y 2) (cbrt.f64 x)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.8b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	49.8b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	52.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))) (sin.f64 (/.f64 x (.f64 y 2))))))
	50.0b	(/.f64 (tan.f64 (.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	38.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.8b	(/.f64 (tan.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))))
	49.7b	(/.f64 (tan.f64 (.f64 (sqrt.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	53.6b	(/.f64 (tan.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 y 2)) (/.f64 x (.f64 y 2))) (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.6b	(/.f64 (.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	38.1b	(/.f64 (tan.f64 (expm1.f64 (log1p.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
▶	28.4b	1
	49.7b	(/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (/.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))))
	36.1b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.4b	(/.f64 (tan.f64 (.f64 x (/.f64 1/2 y))) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 3383 to 2412 computations (28.7% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune34.0ms (0.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	22	22
Picked	1	1
Done	0	0
Total	23	23

Error

25.2b

Counts

23 → 23

Alt Table

Status	Error	Program
	59.9b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (log.f64 (exp.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	36.8b	(/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.2b	(/.f64 (log.f64 (exp.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	57.7b	(/.f64 (tan.f64 (exp.f64 (-.f64 (log.f64 x) (log.f64 (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	37.0b	(/.f64 (tan.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 y 2) (cbrt.f64 x)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.8b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	49.8b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	52.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))) (sin.f64 (/.f64 x (.f64 y 2))))))
	50.0b	(/.f64 (tan.f64 (.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	38.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.8b	(/.f64 (tan.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))))
	49.7b	(/.f64 (tan.f64 (.f64 (sqrt.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	53.6b	(/.f64 (tan.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 y 2)) (/.f64 x (.f64 y 2))) (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.6b	(/.f64 (.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	38.1b	(/.f64 (tan.f64 (expm1.f64 (log1p.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	28.4b	1
	49.7b	(/.f64 (sqrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (/.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (tan.f64 (/.f64 x (*.f64 y 2))))))
▶	36.1b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.4b	(/.f64 (tan.f64 (.f64 x (/.f64 1/2 y))) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 1113 to 813 computations (27% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
✓	28.0b	(cos.f64 (*.f64 1/2 (/.f64 x y)))
	28.2b	(sin.f64 (/.f64 x (*.f64 y 2)))
✓	28.2b	(sin.f64 (*.f64 1/2 (/.f64 x y)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

3 → 90

Calls

3 calls:

5.0ms	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
1.0ms	(sin.f64 (*.f64 1/2 (/.f64 x y)))
1.0ms	(cos.f64 (*.f64 1/2 (/.f64 x y)))

series76.0ms (0.9%)

Counts

3 → 48

Calls

3 calls:

44.0ms	(sin.f64 (*.f64 1/2 (/.f64 x y)))
26.0ms	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
6.0ms	(cos.f64 (*.f64 1/2 (/.f64 x y)))

simplify156.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
413×	`associate-/r*_binary64`
382×	`associate-/l/_binary64`
379×	`associate-/l*_binary64`
359×	`fma-neg_binary64`

Counts

138 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	5292
1	506	5035
2	1245	4984
3	4217	4930
4	4944	4930

prune272.0ms (3.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	229	8	237
Fresh	7	14	21
Picked	1	0	1
Done	0	1	1
Total	237	23	260

Error

25.2b

Counts

260 → 23

Alt Table

Status	Error	Program
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (/.f64 (/.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))) (sin.f64 (/.f64 x (.f64 y 2)))))
	49.7b	(/.f64 (tan.f64 (.f64 (sqrt.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.9b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (log.f64 (exp.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	36.8b	(/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	53.6b	(/.f64 (tan.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 y 2)) (/.f64 x (.f64 y 2))) (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.1b	(/.f64 (tan.f64 (expm1.f64 (log1p.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	28.4b	1
	50.0b	(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	36.6b	(/.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	52.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2))))))
	50.0b	(/.f64 (tan.f64 (.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	36.8b	(/.f64 (tan.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))))
	57.7b	(/.f64 (tan.f64 (exp.f64 (-.f64 (log.f64 x) (log.f64 (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
▶	36.1b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
	37.0b	(/.f64 (tan.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 y 2) (cbrt.f64 x)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	38.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (fma.f64 (.f64 (/.f64 x y) (/.f64 x y)) -1/8 1)) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.4b	(/.f64 (tan.f64 (.f64 x (/.f64 1/2 y))) (sin.f64 (/.f64 x (.f64 y 2))))
	38.8b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 6523 to 4295 computations (34.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
	28.0b	(cos.f64 (*.f64 1/2 (/.f64 x y)))
	28.2b	(sin.f64 (/.f64 x (*.f64 y 2)))
	28.2b	(sin.f64 (*.f64 1/2 (/.f64 x y)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`times-frac_binary64`
83×	`*-un-lft-identity_binary64`
83×	`add-sqr-sqrt_binary64`
83×	`add-cube-cbrt_binary64`
48×	`log-pow_binary64`

Counts

1 → 120

Calls

1 calls:

7.0ms

(/.f64 (/.f64 (sin.f64 (*.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (*.f64 y 2))))

series433.0ms (5.3%)

Counts

1 → 24

Calls

1 calls:

433.0ms

(/.f64 (/.f64 (sin.f64 (*.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (*.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (*.f64 y 2))))

simplify269.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-/l/_binary64`
458×	`fma-def_binary64`
369×	`distribute-rgt-in_binary64`
368×	`associate-/r*_binary64`
358×	`associate-/l*_binary64`

Counts

144 → 283

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	272	7333
1	503	7126
2	1063	7120
3	2737	7114
4	3190	7087
5	4070	7087
6	5285	7087

prune427.0ms (5.3%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	424	7	431
Fresh	4	17	21
Picked	1	0	1
Done	0	1	1
Total	429	25	454

Error

25.2b

Counts

454 → 25

Alt Table

Status	Error	Program
	59.9b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (log.f64 (exp.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	36.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (/.f64 (/.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))) (sin.f64 (/.f64 x (.f64 y 2)))))
	36.6b	(/.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))))) (cbrt.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))))) (/.f64 (sin.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))))))
	49.7b	(/.f64 (tan.f64 (.f64 (sqrt.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	38.4b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (*.f64 1/2 (/.f64 x y)))
	36.8b	(/.f64 (tan.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 y 2))) (cbrt.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (.f64 y 2)))))) (cbrt.f64 (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (sin.f64 (/.f64 x (*.f64 y 2))))))
	57.7b	(/.f64 (tan.f64 (exp.f64 (-.f64 (log.f64 x) (log.f64 (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	38.1b	(/.f64 (tan.f64 (expm1.f64 (log1p.f64 (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	28.4b	1
	36.6b	(/.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (cbrt.f64 (sin.f64 (.f64 1/2 (/.f64 x y))))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.5b	(.f64 (/.f64 (/.f64 1 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2))))))
	37.0b	(/.f64 (tan.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 y 2) (cbrt.f64 x)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 2 y)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 2 y)))))) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 2 y))))) (cbrt.f64 (cos.f64 (.f64 1/2 (/.f64 x y))))))
	36.4b	(/.f64 (tan.f64 (.f64 x (/.f64 1/2 y))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (log.f64 (exp.f64 (cos.f64 (.f64 1/2 (/.f64 x y)))))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	38.8b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	52.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (cos.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))) (sin.f64 (/.f64 x (*.f64 y 2))))))
	50.0b	(/.f64 (tan.f64 (.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) 2))) (sin.f64 (/.f64 x (.f64 y 2))))
	36.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2))))) (.f64 (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (.f64 y 2)))))) (/.f64 (cbrt.f64 (tan.f64 (/.f64 x (.f64 y 2)))) (cbrt.f64 (sin.f64 (/.f64 x (*.f64 y 2))))))
	36.8b	(/.f64 (tan.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) 2))) (sin.f64 (/.f64 x (*.f64 y 2))))
	36.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2)))))) (cbrt.f64 (/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))))
	53.6b	(/.f64 (tan.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 y 2)) (/.f64 x (.f64 y 2))) (/.f64 x (.f64 y 2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	38.7b	(/.f64 (/.f64 (sin.f64 (.f64 1/2 (/.f64 x y))) (fma.f64 (.f64 (/.f64 x y) (/.f64 x y)) -1/8 1)) (sin.f64 (/.f64 x (*.f64 y 2))))

Compiler

Compiled 11163 to 7463 computations (33.1% saved)

regimes1.4s (16.7%)

Accuracy

Total 2.8b remaining (9.9%)

Threshold costs 0b (0%)

Compiler

Compiled 20527 to 14668 computations (28.5% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	26
1	21	26
2	20	26

end1.0ms (0%)

Compiler: Compiled 19 to 16 computations (15.8% saved)

sample3.4s (41.8%)

Algorithm

1×

intervals

Results

966.0ms	1139×	body	2048	valid
613.0ms	1311×	body	1024	valid
505.0ms	4237×	body	128	valid
279.0ms	457×	body	256	valid
249.0ms	851×	body	512	valid
12.0ms	5×	body	4096	valid

Compiler

Compiled 901 to 638 computations (29.2% saved)

Details

analyze1.1s (13.2%)

sample79.0ms (1%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite35.0ms (0.4%)

series151.0ms (1.9%)

simplify115.0ms (1.4%)

prune151.0ms (1.9%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.1%)

prune34.0ms (0.4%)

localize12.0ms (0.1%)

rewrite13.0ms (0.2%)

series76.0ms (0.9%)

simplify156.0ms (1.9%)

prune272.0ms (3.4%)

localize16.0ms (0.2%)

rewrite19.0ms (0.2%)

series433.0ms (5.3%)

simplify269.0ms (3.3%)

prune427.0ms (5.3%)

regimes1.4s (16.7%)

bsearch6.0ms (0.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.4s (41.8%)

Profiling