Details

analyze817.0ms (6.2%)

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
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 53 to 41 computations (22.6% saved)

sample152.0ms (1.1%)

Algorithm

1×

intervals

Results

86.0ms	95×	body	1024	valid
28.0ms	47×	body	512	valid
18.0ms	95×	body	128	valid
7.0ms	19×	body	256	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-neg-out_binary64`
438×	`distribute-lft-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
358×	`associate-*l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	80
2	190	80
3	581	77
4	2012	77
5	4670	77
6	4940	77

prune9.0ms (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

0.4b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))

Status

Error

Program

▶

0.5b

(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (*.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (*.f64 3/2 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))

0.5b

(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))

Compiler

Compiled 254 to 194 computations (23.6% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite452.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

47×	`cancel-sign-sub-inv_binary64`
44×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
30×	`distribute-lft-in_binary64`
30×	`distribute-rgt-in_binary64`

Counts

4 → 128

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
13.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 6675 to 4440 computations (33.5% saved)

series134.0ms (1%)

Error

0.4b

Counts

4 → 24

Calls

4 calls:

42.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
35.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
21.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 2915 to 2214 computations (24% saved)

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

391×	`distribute-rgt-in_binary64`
358×	`distribute-lft-in_binary64`
254×	`associate-r_binary64`
254×	`associate-l_binary64`
212×	`*-commutative_binary64`

Counts

152 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	2938
1	809	2750
2	2375	2539
3	4869	2539
4	4926	2539

prune158.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

0.2b

Counts

107 → 9

Alt Table

Status	Error	Program
	1.1b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (.f64 (cbrt.f64 3/2) (cbrt.f64 3/2)) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 3/2))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (cbrt.f64 (pow.f64 (.f64 (cos.f64 x) (*.f64 3/2 (-.f64 (sqrt.f64 5) 1))) 3)))))
	0.9b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (fabs.f64 (cbrt.f64 5))) (sqrt.f64 (cbrt.f64 5)))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (/.f64 (.f64 (cos.f64 x) 6) (+.f64 (sqrt.f64 5) 1)))))
▶	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1)))) (cbrt.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))))) (cbrt.f64 (.f64 (cos.f64 x) (*.f64 3/2 (-.f64 (sqrt.f64 5) 1))))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (sqrt.f64 (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 3/2 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))

Compiler

Compiled 3693 to 2585 computations (30% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.8b	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite429.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

41×	`add-sqr-sqrt_binary64`
35×	`cancel-sign-sub-inv_binary64`
32×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 118

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
14.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 6451 to 4448 computations (31% saved)

series167.0ms (1.3%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

43.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
35.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
33.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 3276 to 2558 computations (21.9% saved)

simplify128.0ms (1%)

Algorithm

1×	egg-herbie

Rules

494×	`distribute-rgt-in_binary64`
345×	`associate-l_binary64`
337×	`associate-r_binary64`
245×	`cancel-sign-sub-inv_binary64`
234×	`*-commutative_binary64`

Counts

142 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	343	2947
1	851	2612
2	2600	2401
3	4781	2393
4	4922	2393

prune185.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

0.1b

Counts

104 → 8

Alt Table

Status	Error	Program
	1.1b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (.f64 (cbrt.f64 3/2) (cbrt.f64 3/2)) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 3/2))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (cbrt.f64 (pow.f64 (.f64 (cos.f64 x) (*.f64 3/2 (-.f64 (sqrt.f64 5) 1))) 3)))))
	0.9b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (fabs.f64 (cbrt.f64 5))) (sqrt.f64 (cbrt.f64 5)))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (sqrt.f64 (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
▶	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.8b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (cbrt.f64 (pow.f64 (-.f64 3 (sqrt.f64 5)) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))

Compiler

Compiled 3779 to 2690 computations (28.8% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.8b	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))
1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite659.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

35×	`add-sqr-sqrt_binary64`
29×	`cancel-sign-sub-inv_binary64`
28×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
14.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

Compiler

Compiled 6670 to 4695 computations (29.6% saved)

series298.0ms (2.3%)

Error

0.1b

Counts

4 → 34

Calls

4 calls:

102.0ms	(+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))
49.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
38.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
32.0ms	(.f64 (sqrt.f64 3/2) (.f64 (*.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2)))

Compiler

Compiled 5004 to 3944 computations (21.2% saved)

simplify155.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

519×	`cancel-sign-sub-inv_binary64`
427×	`associate-r_binary64`
425×	`associate-l_binary64`
277×	`*-commutative_binary64`
201×	`sub-neg_binary64`

Counts

145 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	372	3832
1	1011	3416
2	3384	3212
3	4704	3204
4	4937	3204

prune223.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Error

0.1b

Counts

113 → 8

Alt Table

Status	Error	Program
	0.9b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (fabs.f64 (cbrt.f64 5))) (sqrt.f64 (cbrt.f64 5)))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (cbrt.f64 (pow.f64 (+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3)))) 3))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3)) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 (cos.f64 y) (+.f64 (cos.f64 y) (cos.f64 x))))))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (sqrt.f64 (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
▶	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (log.f64 (exp.f64 (+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.8b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (cbrt.f64 (pow.f64 (-.f64 3 (sqrt.f64 5)) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))

Compiler

Compiled 4592 to 3271 computations (28.8% saved)

localize37.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (*.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(*.f64 3/2 (-.f64 (sqrt.f64 5) 1))
1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite536.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

52×	`add-sqr-sqrt_binary64`
47×	`cancel-sign-sub-inv_binary64`
39×	`*-un-lft-identity_binary64`
34×	`distribute-lft-in_binary64`
34×	`distribute-rgt-in_binary64`

Counts

4 → 137

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
13.0ms	(+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (*.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))
10.0ms	(*.f64 3/2 (-.f64 (sqrt.f64 5) 1))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

Compiler

Compiled 7531 to 5139 computations (31.8% saved)

series225.0ms (1.7%)

Error

0.1b

Counts

4 → 29

Calls

4 calls:

79.0ms	(+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (*.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))
44.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
35.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(*.f64 3/2 (-.f64 (sqrt.f64 5) 1))

Compiler

Compiled 3832 to 2921 computations (23.8% saved)

simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

353×	`cancel-sign-sub-inv_binary64`
340×	`times-frac_binary64`
331×	`associate-l_binary64`
326×	`associate-r_binary64`
236×	`*-commutative_binary64`

Counts

166 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	358	3768
1	931	3543
2	3083	3340
3	4473	3328
4	4986	3328

prune249.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Error

0.1b

Counts

135 → 7

Alt Table

Status	Error	Program
	0.9b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (fabs.f64 (cbrt.f64 5))) (sqrt.f64 (cbrt.f64 5)))))) (.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (cbrt.f64 (pow.f64 (+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3)))) 3))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3)) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 (cos.f64 y) (+.f64 (cos.f64 y) (cos.f64 x))))))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 (sqrt.f64 5) 3)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (sqrt.f64 (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (log.f64 (exp.f64 (+.f64 (.f64 (cos.f64 x) (.f64 3/2 (-.f64 (sqrt.f64 5) 1))) (*.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))))))
	0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) 3)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (+.f64 (.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5)))) (.f64 (sqrt.f64 3/2) (.f64 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 3/2))))))
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (+.f64 3 (log.f64 (exp.f64 (+.f64 (.f64 (cos.f64 x) (.f64 (.f64 (sqrt.f64 3/2) (sqrt.f64 (+.f64 (sqrt.f64 5) -1))) (.f64 (sqrt.f64 3/2) (sqrt.f64 (+.f64 (sqrt.f64 5) -1))))) (.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3))))))))

Compiler

Compiled 4238 to 2954 computations (30.3% saved)

regimes2.3s (17.1%)

Accuracy

Total 0.2b remaining (60.8%)

Threshold costs 0.2b (60.8%)

Compiler

Compiled 48098 to 37402 computations (22.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	105
1	61	105
2	75	105
3	85	105
4	92	105
5	94	105
6	92	105

end2.0ms (0%)

Compiler: Compiled 67 to 55 computations (17.9% saved)

sample5.5s (41.4%)

Algorithm

1×

intervals

Results

3.1s	3432×	body	1024	valid
871.0ms	1419×	body	512	valid
507.0ms	2577×	body	128	valid
223.0ms	554×	body	256	valid
27.0ms	18×	body	2048	valid

Compiler

Compiled 535 to 417 computations (22.1% saved)

Details

analyze817.0ms (6.2%)

sample152.0ms (1.1%)

simplify53.0ms (0.4%)

prune9.0ms (0.1%)

localize34.0ms (0.3%)

rewrite452.0ms (3.4%)

series134.0ms (1%)

simplify133.0ms (1%)

prune158.0ms (1.2%)

localize39.0ms (0.3%)

rewrite429.0ms (3.2%)

series167.0ms (1.3%)

simplify128.0ms (1%)

prune185.0ms (1.4%)

localize36.0ms (0.3%)

rewrite659.0ms (5%)

series298.0ms (2.3%)

simplify155.0ms (1.2%)

prune223.0ms (1.7%)

localize37.0ms (0.3%)

rewrite536.0ms (4.1%)

series225.0ms (1.7%)

simplify164.0ms (1.2%)

prune249.0ms (1.9%)

regimes2.3s (17.1%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample5.5s (41.4%)

Profiling