Details

analyze1.2s (15.1%)

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)

sample3.9s (48.7%)

Results

1.4s	1207×	body	2048	valid
1.1s	1368×	body	1024	valid
717.0ms	4294×	body	128	valid
427.0ms	863×	body	512	valid
172.0ms	516×	body	256	valid
30.0ms	8×	body	4096	valid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 1

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

35.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.6b	(/.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 3 expressions with local error:

New	Error	Program
✓	7.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	27.9b	(sin.f64 (/.f64 x (*.f64 y 2)))
✓	28.4b	(tan.f64 (/.f64 x (*.f64 y 2)))

series74.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

35.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
32.0ms	(tan.f64 (/.f64 x (*.f64 y 2)))
6.0ms	(sin.f64 (/.f64 x (*.f64 y 2)))

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`prod-diff_binary64`
522×	`log-prod_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	193	38
2	2642	38

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

55.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
55.0ms	(sin.f64 (/.f64 x (*.f64 y 2)))
55.0ms	(tan.f64 (/.f64 x (*.f64 y 2)))

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

363×	`associate-/r/_binary64`
360×	`cancel-sign-sub-inv_binary64`
359×	`times-frac_binary64`
339×	`associate-/l/_binary64`
215×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1410
1	187	1392
2	544	1326
3	2662	1299

Stop Event

1×	node limit

Counts

159 → 110

prune219.0ms (2.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	92	18	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	18	111

Error

24.9b

Counts

111 → 18

Alt Table

Status	Error	Program
	35.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	53.9b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
▶	27.6b	1
	35.6b	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 3)
	37.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	36.3b	(/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.3b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.4b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
	30.8b	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)
	54.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	49.3b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (cbrt.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	61.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	36.3b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	60.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	37.9b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))

Compiler

Compiled 3175 to 2144 computations (32.5% saved)

localize0.0ms (0%)

prune30.0ms (0.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	17	17
Picked	1	1
Done	0	0
Total	18	18

Error

24.9b

Counts

18 → 18

Alt Table

Status	Error	Program
	35.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	53.9b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
✓	27.6b	1
	35.6b	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 3)
	37.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	36.3b	(/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.3b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.4b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
▶	30.8b	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)
	54.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	49.3b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (cbrt.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	61.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	36.3b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	60.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	37.9b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))

Compiler

Compiled 901 to 645 computations (28.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 x (/.f64 y x))
✓	1.5b	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)

series24.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)
9.0ms	(/.f64 x (/.f64 y x))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

471×	`log-prod_binary64`
242×	`pow2_binary64`
170×	`pow1/3_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	191	21
2	2526	21

Stop Event

1×	node limit

Counts

2 → 72

Calls

2 calls:

44.0ms	(/.f64 x (/.f64 y x))
44.0ms	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/l*_binary64`
427×	`associate-/l/_binary64`
423×	`associate-/r*_binary64`
399×	`unswap-sqr_binary64`
325×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	498
1	25	462
2	51	462
3	146	462
4	762	462
5	4776	462

Stop Event

1×	node limit

Counts

120 → 78

prune97.0ms (1.2%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	16	16
Picked	0	1	1
Done	0	1	1
Total	78	18	96

Error

24.9b

Counts

96 → 18

Alt Table

Status	Error	Program
	35.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	53.9b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
✓	27.6b	1
	35.6b	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 3)
	37.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
▶	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	36.3b	(/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.3b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.4b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
✓	30.8b	(fma.f64 (/.f64 1/8 y) (/.f64 x (/.f64 y x)) 1)
	54.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	49.3b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (cbrt.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	61.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))
	36.3b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	60.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	37.9b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))

Compiler

Compiled 2064 to 1252 computations (39.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 2)
✓	7.2b	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))
✓	27.9b	(sin.f64 (*.f64 (/.f64 x y) 1/2))
✓	28.4b	(tan.f64 (*.f64 (/.f64 x y) 1/2))

series389.0ms (4.9%)

Counts

4 → 96

Calls

4 calls:

306.0ms	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 2)
54.0ms	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))
19.0ms	(tan.f64 (*.f64 (/.f64 x y) 1/2))
10.0ms	(sin.f64 (*.f64 (/.f64 x y) 1/2))

rewrite68.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

292×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
194×	`log-pow_binary64`
136×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	63
1	255	63
2	3188	63

Stop Event

1×	node limit

Counts

4 → 99

Calls

4 calls:

66.0ms	(pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 2)
66.0ms	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))
66.0ms	(sin.f64 (*.f64 (/.f64 x y) 1/2))
66.0ms	(tan.f64 (*.f64 (/.f64 x y) 1/2))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

407×	`times-frac_binary64`
383×	`associate-/l/_binary64`
360×	`cancel-sign-sub-inv_binary64`
215×	`fma-neg_binary64`
204×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1878
1	233	1854
2	655	1782
3	3089	1728

Stop Event

1×	node limit

Counts

195 → 130

prune375.0ms (4.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	219	12	231
Fresh	7	8	15
Picked	1	0	1
Done	1	1	2
Total	228	21	249

Error

24.6b

Counts

249 → 21

Alt Table

Status	Error	Program
	53.9b	(.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	59.3b	(/.f64 (log.f64 (+.f64 1 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 3)) 2))
	53.9b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	36.5b	(.f64 (cbrt.f64 1) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (/.f64 (.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
✓	27.6b	1
	36.2b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 1) 2))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) 2) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	37.6b	(.f64 (cbrt.f64 (/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	49.3b	(.f64 (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (sqrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (cbrt.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	36.4b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) (.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) (/.f64 1 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) 2))
	37.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 (pow.f64 (/.f64 x y) 3) -1/48 (.f64 1/2 (/.f64 x y))))
	36.2b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)) (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	61.5b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 2))
	60.2b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	59.4b	(/.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))))) (sin.f64 (/.f64 x (*.f64 y 2))))
	54.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))) 2))
	35.6b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) 4)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) 2) (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2))))))) 2))
	61.4b	(.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (-.f64 (.f64 (sin.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (cos.f64 1)) (.f64 (cos.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 1))))) 2))
	36.5b	(+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))) (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))

Compiler

Compiled 9731 to 6293 computations (35.3% saved)

regimes917.0ms (11.4%)

Accuracy

Total 3.1b remaining (10.6%)

Threshold costs 0b (0%)

Counts

118 → 1

Compiler

Compiled 17396 to 12253 computations (29.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

end409.0ms (5.1%)

Compiler: Compiled 765 to 535 computations (30.1% saved)

Details

analyze1.2s (15.1%)

sample3.9s (48.7%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series74.0ms (0.9%)

rewrite56.0ms (0.7%)

simplify49.0ms (0.6%)

prune219.0ms (2.7%)

localize0.0ms (0%)

prune30.0ms (0.4%)

localize6.0ms (0.1%)

series24.0ms (0.3%)

rewrite45.0ms (0.6%)

simplify48.0ms (0.6%)

prune97.0ms (1.2%)

localize14.0ms (0.2%)

series389.0ms (4.9%)

rewrite68.0ms (0.8%)

simplify57.0ms (0.7%)

prune375.0ms (4.7%)

regimes917.0ms (11.4%)

simplify2.0ms (0%)

end409.0ms (5.1%)

Profiling