Details

analyze1.3s (17.6%)

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)

sample3.8s (52.2%)

Results

1.3s	1095×	body	2048	valid
1.0s	1412×	body	1024	valid
820.0ms	4364×	body	128	valid
436.0ms	906×	body	512	valid
173.0ms	475×	body	256	valid
14.0ms	4×	body	4096	valid

Compiler

Compiled 32 to 24 computations (25% saved)

preprocess18.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	20	40
2	24	40
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify7.0ms (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

prune3.0ms (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

37.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	5.0b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))
✓	32.8b	(tan.f64 (/.f64 x (*.f64 y 2)))
✓	32.9b	(sin.f64 (/.f64 x (*.f64 y 2)))

series70.0ms (1%)

Counts

3 → 72

Calls

18 calls:

8.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	x	inf
7.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	y	0
7.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	x	-inf
6.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	y	-inf
6.0ms	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sin.f64 (/.f64 x (.f64 y 2))))	y	inf

rewrite60.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	193	38
2	2622	38

Stop Event

1×	node limit

Counts

3 → 87

simplify52.0ms (0.7%)

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	2664	1299

Stop Event

1×	node limit

Counts

159 → 110

prune136.0ms (1.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	91	19	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	19	111

Error

29.8b

Counts

111 → 19

Alt Table

Status	Error	Program
	40.0b	(.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)))))
	38.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)))
	61.5b	(/.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))))
▶	32.9b	1
	53.3b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	37.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	59.6b	(/.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)))))))
	53.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	40.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 1/2 (/.f64 x y) (.f64 (pow.f64 (/.f64 x y) 3) -1/48)))
	51.2b	(/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	40.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	51.3b	(.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)))))
	38.4b	(/.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))))
	59.0b	(/.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))))
	37.9b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))))
	38.1b	(.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)))))
	38.4b	(/.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))))

Compiler

Compiled 3207 to 2175 computations (32.2% saved)

localize0.0ms (0%)

prune28.0ms (0.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	18	18
Picked	1	1
Done	0	0
Total	19	19

Error

29.8b

Counts

19 → 19

Alt Table

Status	Error	Program
	40.0b	(.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)))))
	38.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)))
	61.5b	(/.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))))
✓	32.9b	1
	53.3b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
▶	37.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	59.6b	(/.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)))))))
	53.5b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	40.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 1/2 (/.f64 x y) (.f64 (pow.f64 (/.f64 x y) 3) -1/48)))
	51.2b	(/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	40.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	51.3b	(.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)))))
	38.4b	(/.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))))
	59.0b	(/.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))))
	37.9b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))))
	38.1b	(.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)))))
	38.4b	(/.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))))

Compiler

Compiled 933 to 679 computations (27.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
✓	5.0b	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))
✓	32.8b	(tan.f64 (*.f64 (/.f64 x y) 1/2))
✓	32.9b	(sin.f64 (*.f64 (/.f64 x y) 1/2))

series109.0ms (1.5%)

Counts

4 → 96

Calls

24 calls:

9.0ms	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))	y	0
9.0ms	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))	x	inf
8.0ms	(/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))	x	-inf
7.0ms	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))	y	0
7.0ms	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (.f64 (/.f64 x y) 1/2)))))	x	-inf

rewrite65.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log-prod_binary64`
327×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
165×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
1	215	58
2	2770	58

Stop Event

1×	node limit

Counts

4 → 136

simplify54.0ms (0.8%)

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	1818
1	187	1794
2	544	1722
3	2664	1668

Stop Event

1×	node limit

Counts

232 → 123

prune145.0ms (2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	4	13	17
Picked	1	0	1
Done	0	1	1
Total	122	20	142

Error

29.8b

Counts

142 → 20

Alt Table

Status	Error	Program
	38.4b	(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (log1p.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	59.0b	(/.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))))
	38.3b	(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 3) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	40.0b	(.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)))))
	38.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)))
	59.0b	(log1p.f64 (expm1.f64 (/.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 (/.f64 x y) 1/2)))))
▶	37.9b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	61.5b	(/.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))))
✓	32.9b	1
	53.5b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))))
	53.3b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	51.2b	(/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	40.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	61.6b	(log1p.f64 (expm1.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))))))
	38.1b	(.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)))))
	59.6b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))))
	59.6b	(/.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)))))))
	40.7b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (fma.f64 1/2 (/.f64 x y) (.f64 (pow.f64 (/.f64 x y) 3) -1/48)))
	38.4b	(/.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))))

Compiler

Compiled 3800 to 2567 computations (32.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(log1p.f64 (expm1.f64 (tan.f64 (*.f64 (/.f64 x y) 1/2))))
✓	5.0b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))
	32.8b	(tan.f64 (*.f64 (/.f64 x y) 1/2))
	32.9b	(sin.f64 (/.f64 x (*.f64 y 2)))

series67.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

10.0ms	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))	y	0
7.0ms	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))	x	-inf
7.0ms	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))	x	inf
6.0ms	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sin.f64 (/.f64 x (.f64 y 2))))	y	-inf
6.0ms	(log1p.f64 (expm1.f64 (tan.f64 (*.f64 (/.f64 x y) 1/2))))	x	-inf

rewrite57.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
195×	`log-pow_binary64`
140×	`add-sqr-sqrt_binary64`
137×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	283	29
2	3731	29

Stop Event

1×	node limit

Counts

2 → 56

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
784×	`associate-/r/_binary64`
443×	`associate-/l/_binary64`
314×	`times-frac_binary64`
294×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	966
1	147	960
2	398	927
3	1949	894
4	4228	894

Stop Event

1×	node limit

Counts

104 → 75

prune138.0ms (1.9%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	130	10	140
Fresh	5	13	18
Picked	1	0	1
Done	0	1	1
Total	136	24	160

Error

29.6b

Counts

160 → 24

Alt Table

Status	Error	Program
	38.3b	(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 3) (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	59.6b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (+.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)))))))
	38.3b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 2)))
	39.9b	(/.f64 (/.f64 (sin.f64 (/.f64 1/2 (/.f64 y x))) (cos.f64 (/.f64 1/2 (/.f64 y x)))) (sin.f64 (/.f64 x (*.f64 y 2))))
	61.5b	(/.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))))
✓	32.9b	1
	53.5b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))))
	59.0b	(/.f64 (log1p.f64 (expm1.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))))
	38.1b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) 3))
	40.9b	(/.f64 (.f64 1/2 (/.f64 x y)) (sin.f64 (/.f64 x (.f64 y 2))))
	53.3b	(/.f64 (sqrt.f64 (pow.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) 2)) (sin.f64 (/.f64 x (.f64 y 2))))
	59.6b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sin.f64 (*.f64 (/.f64 x y) 1/2)))))))
	32.9b	(/.f64 1 (cos.f64 (/.f64 1/2 (/.f64 y x))))
	59.6b	(/.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)))))))
	51.2b	(/.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))) (/.f64 (cos.f64 (.f64 (/.f64 x y) 1/2)) (sqrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2))))) (sin.f64 (/.f64 x (.f64 y 2))))
	40.8b	(/.f64 (tan.f64 (/.f64 x (.f64 y 2))) (.f64 1/2 (/.f64 x y)))
	60.9b	(/.f64 (/.f64 (-.f64 (sin.f64 (exp.f64 (log1p.f64 (/.f64 x y)))) (sin.f64 1)) (+.f64 (cos.f64 (exp.f64 (log1p.f64 (/.f64 x y)))) (cos.f64 1))) (sin.f64 (/.f64 x (*.f64 y 2))))
	59.0b	(/.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))))
	59.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 (/.f64 x y) 1/2))) 2) (cbrt.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 (/.f64 x y)))))) (cbrt.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (sin.f64 (*.f64 (/.f64 x y) 1/2)))))
	59.8b	(.f64 (/.f64 1 (cbrt.f64 (-.f64 1/2 (.f64 1/2 (cos.f64 (/.f64 x y)))))) (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (cbrt.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))
	59.6b	(log1p.f64 (expm1.f64 (/.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)) (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)))))))
	53.5b	(/.f64 (log1p.f64 (expm1.f64 (tan.f64 (.f64 (/.f64 x y) 1/2)))) (sqrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 x y) 1/2)) 2)))
	38.4b	(/.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))))
	61.6b	(log1p.f64 (expm1.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))))))

Compiler

Compiled 3563 to 2402 computations (32.6% saved)

regimes664.0ms (9.2%)

Accuracy

Total 3.1b remaining (10.9%)

Threshold costs 0b (0%)

Counts

107 → 1

Compiler

Compiled 11754 to 8620 computations (26.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	14	16

Stop Event

1×

saturated

end415.0ms (5.7%)

Stop Event

1×

fuel

Compiler

Compiled 632 to 464 computations (26.6% saved)

Details

analyze1.3s (17.6%)

sample3.8s (52.2%)

preprocess18.0ms (0.2%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series70.0ms (1%)

rewrite60.0ms (0.8%)

simplify52.0ms (0.7%)

prune136.0ms (1.9%)

localize0.0ms (0%)

prune28.0ms (0.4%)

localize13.0ms (0.2%)

series109.0ms (1.5%)

rewrite65.0ms (0.9%)

simplify54.0ms (0.8%)

prune145.0ms (2%)

localize17.0ms (0.2%)

series67.0ms (0.9%)

rewrite57.0ms (0.8%)

simplify48.0ms (0.7%)

prune138.0ms (1.9%)

regimes664.0ms (9.2%)

simplify3.0ms (0%)

end415.0ms (5.7%)

Profiling