Details

analyze1.3s (9.4%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample135.0ms (1%)

Algorithm

1×

intervals

Results

37.0ms	66×	body	1024	valid
35.0ms	63×	body	1024	invalid
16.0ms	149×	body	128	valid
9.0ms	31×	body	512	valid
6.0ms	20×	body	512	invalid
3.0ms	25×	body	128	invalid
2.0ms	11×	body	256	invalid
2.0ms	10×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune7.0ms (0.1%)

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

0.9b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	1.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 89 to 60 computations (32.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite240.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

76×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

4 → 176

Calls

4 calls:

13.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 4179 to 2195 computations (47.5% saved)

series97.0ms (0.7%)

Error

0.8b

Counts

4 → 26

Calls

4 calls:

27.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
23.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
19.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
12.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1512 to 1118 computations (26.1% saved)

simplify168.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

644×	`associate-*l/_binary64`
554×	`fma-def_binary64`
476×	`associate-/l*_binary64`
419×	`associate-*r/_binary64`
176×	`*-commutative_binary64`

Counts

202 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	3999
1	587	3587
2	1693	3566
3	4365	3562
4	4973	3562
5	4967	3562

prune121.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	119	13	132
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	120	14	134

Error

0.5b

Counts

134 → 14

Alt Table

Status	Error	Program
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
▶	1.0b	(+.f64 (.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	20.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.1b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (.f64 (.f64 a1 a1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 (cbrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	22.3b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a1 6))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.1b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))))
	30.5b	(fma.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (fma.f64 a2 (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (fma.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) -1/720 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) -1/2))) (/.f64 a2 (sqrt.f64 2)))))
	1.1b	(+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.1b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))))))
	1.0b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	1.2b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) 1) (.f64 (.f64 a2 a2) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))
	16.0b	(+.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 (.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))

Compiler

Compiled 2995 to 1763 computations (41.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite266.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

76×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
61×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`

Counts

4 → 173

Calls

4 calls:

8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
7.0ms	(*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 4093 to 2307 computations (43.6% saved)

series91.0ms (0.7%)

Error

0.5b

Counts

4 → 26

Calls

4 calls:

30.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
19.0ms	(*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
10.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
8.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1504 to 1105 computations (26.5% saved)

simplify197.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
548×	`associate-*l/_binary64`
469×	`associate-/l*_binary64`
451×	`associate-*r/_binary64`
172×	`associate-l_binary64`

Counts

199 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	3875
1	547	3576
2	1699	3443
3	4255	3411
4	4971	3411
5	4958	3411

prune101.0ms (0.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Error

0.5b

Counts

126 → 14

Alt Table

Status	Error	Program
	30.5b	(fma.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (fma.f64 a2 (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (fma.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) -1/720 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) -1/2))) (/.f64 a2 (sqrt.f64 2)))))
	1.0b	(+.f64 (.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
	20.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.1b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
▶	0.9b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.1b	(+.f64 (.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)) (.f64 a2 a2)))
	1.4b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 2)))) (.f64 (.f64 a1 a1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 (cbrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.4b	(fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	16.0b	(+.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 (.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	16.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.1b	(+.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.1b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))))
	16.1b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (sqrt.f64 2)))))))

Compiler

Compiled 2523 to 1566 computations (37.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
0.3b	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite377.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

81×	`add-sqr-sqrt_binary64`
78×	`times-frac_binary64`
68×	`add-exp-log_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`

Counts

4 → 193

Calls

4 calls:

17.0ms	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
14.0ms	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
8.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 6583 to 4467 computations (32.1% saved)

series116.0ms (0.9%)

Error

0.5b

Counts

4 → 29

Calls

4 calls:

30.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
26.0ms	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
23.0ms	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
13.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1949 to 1511 computations (22.5% saved)

simplify223.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
295×	`associate-l_binary64`
279×	`associate-*l/_binary64`
248×	`associate-*r/_binary64`
240×	`associate-r_binary64`

Counts

222 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	336	7122
1	867	4801
2	3245	4653
3	4564	4617
4	4959	4617
5	4980	4617

prune180.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	157	9	166
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	167	13	180

Error

0.0b

Counts

180 → 13

Alt Table

Status	Error	Program
	30.5b	(fma.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a2 (fma.f64 a2 (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (fma.f64 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) -1/720 (.f64 (/.f64 (.f64 th th) (sqrt.f64 2)) -1/2))) (/.f64 a2 (sqrt.f64 2)))))
	1.1b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))))
	20.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.1b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
▶	0.5b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) a2))
	1.3b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (cbrt.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	0.9b	(+.f64 (.f64 (.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cos.f64 th) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	1.1b	(+.f64 (.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) (.f64 (cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)) (.f64 a2 a2)))
	1.6b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.0b	(+.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 a1 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.9b	(+.f64 (/.f64 (.f64 a1 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	12.0b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (sqrt.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (sqrt.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.0b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))

Compiler

Compiled 3922 to 2653 computations (32.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
0.3b	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
0.3b	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite373.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

85×	`add-sqr-sqrt_binary64`
78×	`times-frac_binary64`
61×	`add-exp-log_binary64`
56×	`associate-r_binary64`
55×	`*-un-lft-identity_binary64`

Counts

4 → 190

Calls

4 calls:

17.0ms	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
14.0ms	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
9.0ms	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
3.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 6479 to 4579 computations (29.3% saved)

series109.0ms (0.8%)

Error

0.0b

Counts

4 → 29

Calls

4 calls:

26.0ms	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
24.0ms	(.f64 (.f64 (/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1)
20.0ms	(.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
12.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1925 to 1478 computations (23.2% saved)

simplify211.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

503×	`fma-def_binary64`
328×	`associate-l_binary64`
272×	`associate-*r/_binary64`
249×	`associate-r_binary64`
246×	`associate-*l/_binary64`

Counts

219 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	6864
1	829	4632
2	3295	4486
3	4569	4486
4	4992	4486
5	4983	4486

prune146.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	152	11	163

Error

0.0b

Counts

163 → 11

Alt Table

Status	Error	Program
	20.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a2 6))))
	1.1b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.1b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))))))
	0.8b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (.f64 (.f64 (cbrt.f64 a2) (cbrt.f64 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (cbrt.f64 a2))) a2))
	0.5b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (*.f64 (/.f64 a2 (sqrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))) a2))
	0.9b	(+.f64 (.f64 (.f64 (/.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cos.f64 th) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.5b	(+.f64 (.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) (.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) a2))
	1.6b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
	1.0b	(+.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 a1 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	0.9b	(+.f64 (/.f64 (.f64 a1 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
	1.0b	(+.f64 (.f64 (.f64 (/.f64 a1 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))) a1) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))

Compiler

Compiled 2840 to 1954 computations (31.2% saved)

regimes4.7s (35.4%)

Accuracy

Total 0.4b remaining (88.5%)

Threshold costs 0.4b (88.5%)

Compiler

Compiled 105756 to 76300 computations (27.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	24	55
2	24	55

end7.0ms (0.1%)

Compiler: Compiled 108 to 87 computations (19.4% saved)

sample4.1s (31%)

Algorithm

1×

intervals

Results

965.0ms	1903×	body	1024	valid
829.0ms	1644×	body	1024	invalid
484.0ms	4735×	body	128	valid
292.0ms	938×	body	512	valid
248.0ms	798×	body	512	invalid
96.0ms	422×	body	256	valid
89.0ms	426×	body	256	invalid
76.0ms	631×	body	128	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 431 to 333 computations (22.7% saved)

Details

analyze1.3s (9.4%)

sample135.0ms (1%)

simplify13.0ms (0.1%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite240.0ms (1.8%)

series97.0ms (0.7%)

simplify168.0ms (1.3%)

prune121.0ms (0.9%)

localize11.0ms (0.1%)

rewrite266.0ms (2%)

series91.0ms (0.7%)

simplify197.0ms (1.5%)

prune101.0ms (0.8%)

localize17.0ms (0.1%)

rewrite377.0ms (2.8%)

series116.0ms (0.9%)

simplify223.0ms (1.7%)

prune180.0ms (1.3%)

localize17.0ms (0.1%)

rewrite373.0ms (2.8%)

series109.0ms (0.8%)

simplify211.0ms (1.6%)

prune146.0ms (1.1%)

regimes4.7s (35.4%)

simplify5.0ms (0%)

end7.0ms (0.1%)

sample4.1s (31%)

Profiling