Details

analyze1.1s (7.7%)

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)

sample8.4s (58.6%)

Results

5.7s	3651×	body	1024	valid
1.4s	1449×	body	512	valid
813.0ms	2556×	body	128	valid
386.0ms	579×	body	256	valid
61.0ms	21×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
350×	`unsub-neg_binary64`
270×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	74
2	211	74
3	809	73
4	3815	73

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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 (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

0.4b

(/.f64 (fma.f64 (sqrt.f64 2) (*.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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 (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 298 to 221 computations (25.8% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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)))
✓	0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
✓	1.0b	(-.f64 3 (sqrt.f64 5))
✓	1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

series62.0ms (0.4%)

Counts

4 → 56

Calls

4 calls:

39.0ms	(.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)))
16.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
6.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

rewrite39.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`add-sqr-sqrt_binary64`
245×	`log1p-expm1-u_binary64`
245×	`expm1-log1p-u_binary64`
243×	`add-cbrt-cube_binary64`
237×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	69
1	506	69

Stop Event

1×	node limit

Counts

4 → 73

Calls

4 calls:

36.0ms	(.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)))
36.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
36.0ms	(-.f64 3 (sqrt.f64 5))
36.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

719×	`cancel-sign-sub-inv_binary64`
421×	`associate--l+_binary64`
331×	`fma-neg_binary64`
231×	`fma-def_binary64`
228×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	1953
1	576	1877
2	2240	1789

Stop Event

1×	node limit

Counts

129 → 123

prune245.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

0.2b

Counts

125 → 7

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (+.f64 2 (.f64 (+.f64 (sin.f64 x) (.f64 -1/16 (sin.f64 y))) (.f64 (sqrt.f64 2) (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (-.f64 (sin.f64 y) (.f64 1/16 (sin.f64 x))))))) (.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)))))
	0.5b	(/.f64 (+.f64 2 (log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) (-.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 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.7b	(/.f64 (+.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))))) 1)) (.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 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)))) (-.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)))))
	0.5b	(/.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 (log.f64 (exp.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 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))

Compiler

Compiled 8013 to 5601 computations (30.1% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (+.f64 (sin.f64 x) (.f64 -1/16 (sin.f64 y))) (.f64 (sqrt.f64 2) (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (-.f64 (sin.f64 y) (*.f64 1/16 (sin.f64 x))))))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (-.f64 (sin.f64 y) (*.f64 1/16 (sin.f64 x)))))
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

series80.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

41.0ms

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

39.0ms

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

rewrite34.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
207×	`add-cbrt-cube_binary64`
202×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	65
1	426	63

Stop Event

1×	node limit

Counts

2 → 30

Calls

2 calls:

33.0ms

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

33.0ms

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

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

879×	`cancel-sign-sub-inv_binary64`
405×	`fma-neg_binary64`
266×	`fma-def_binary64`
258×	`associate-r_binary64`
231×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2201
1	575	2164
2	2365	2056

Stop Event

1×	node limit

Counts

78 → 67

prune311.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Error

0.2b

Counts

134 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (+.f64 2 (.f64 (+.f64 (sin.f64 x) (.f64 -1/16 (sin.f64 y))) (.f64 (sqrt.f64 2) (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (-.f64 (sin.f64 y) (.f64 1/16 (sin.f64 x))))))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5)))) 2) (cos.f64 y)))))
▶	0.4b	(/.f64 (+.f64 2 (log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (.f64 -1/16 (sin.f64 x))))))) (.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)))))
	0.7b	(/.f64 (+.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (.f64 -1/16 (sin.f64 x)))) (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))))) 1)) (.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 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (+.f64 2 (.f64 (+.f64 (sin.f64 x) (.f64 -1/16 (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (.f64 -1/16 (sin.f64 x))))) 3))) (.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 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))

Compiler

Compiled 8305 to 5797 computations (30.2% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.7b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	3.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (*.f64 -1/16 (sin.f64 x))))))

series1.3s (9.2%)

Counts

2 → 32

Calls

2 calls:

1.3s

(log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (*.f64 -1/16 (sin.f64 x))))))

13.0ms

(*.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))

rewrite37.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
201×	`add-cbrt-cube_binary64`
200×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	419	48

Stop Event

1×	node limit

Counts

2 → 43

Calls

2 calls:

35.0ms

(*.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))

35.0ms

(log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (*.f64 -1/16 (sin.f64 x))))))

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

647×	`cancel-sign-sub-inv_binary64`
396×	`associate--l+_binary64`
310×	`fma-neg_binary64`
220×	`fma-def_binary64`
217×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1592
1	511	1546
2	2026	1460

Stop Event

1×	node limit

Counts

75 → 77

prune401.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Error

0.2b

Counts

143 → 7

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (+.f64 2 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.f64 y))))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.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 (fma.f64 -1/16 (sin.f64 x) (sin.f64 y)) (log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.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)))))
	0.7b	(/.f64 (+.f64 2 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (fma.f64 -1/16 (sin.f64 x) (sin.f64 y))))))) 1)) (.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)))))
	0.5b	(/.f64 (+.f64 2 (+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 2 (fma.f64 -1/16 (sin.f64 x) (sin.f64 y)))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.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 (sin.f64 x) (.f64 -1/16 (sin.f64 y))) (pow.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y))) (+.f64 (sin.f64 y) (.f64 -1/16 (sin.f64 x))))) 3))) (.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 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))

Compiler

Compiled 9151 to 6359 computations (30.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y))))
✓	0.7b	(/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3)
✓	1.0b	(-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3))
	1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

series36.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

31.0ms

(*.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y))))

5.0ms

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

0.0ms

(-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3))

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

290×	`add-cbrt-cube_binary64`
290×	`log1p-expm1-u_binary64`
290×	`expm1-log1p-u_binary64`
282×	`add-log-exp_binary64`
281×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	57
1	593	57

Stop Event

1×	node limit

Counts

3 → 46

Calls

3 calls:

35.0ms

(*.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y))))

35.0ms

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

35.0ms

(-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3))

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-l_binary64`
498×	`associate-r_binary64`
476×	`cancel-sign-sub-inv_binary64`
454×	`associate--l+_binary64`
203×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	1324
1	448	1284
2	1684	1230

Stop Event

1×	node limit

Counts

82 → 73

prune340.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	6	116
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

0.1b

Counts

123 → 10

Alt Table

Status	Error	Program
	16.2b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 3/2)) 2) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (+.f64 2 (.f64 (fma.f64 -1/16 (sin.f64 x) (sin.f64 y)) (log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.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 (fma.f64 (sqrt.f64 2) (log.f64 (pow.f64 (pow.f64 (exp.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (+.f64 2 (+.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.f64 y))))) (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.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)))))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 3/2)) 3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (+.f64 2 (+.f64 (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 2 (fma.f64 -1/16 (sin.f64 x) (sin.f64 y)))))) (log.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 y) -1/16 (sin.f64 x))) (.f64 (sqrt.f64 2) (-.f64 (cos.f64 x) (cos.f64 y)))) (fma.f64 -1/16 (sin.f64 x) (sin.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)))))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))))) 1) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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 (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 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 3/2) 3)) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 3/2)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Compiler

Compiled 6940 to 4624 computations (33.4% saved)

regimes1.1s (8%)

Accuracy

Total 0.3b remaining (61.8%)

Threshold costs 0.3b (61.8%)

Counts

192 → 1

Compiler

Compiled 31034 to 24169 computations (22.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
10×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	71
1	44	71
2	64	71
3	78	71
4	88	71
5	91	71

Stop Event

1×

saturated

end369.0ms (2.6%)

Compiler: Compiled 667 to 497 computations (25.5% saved)

Details

analyze1.1s (7.7%)

sample8.4s (58.6%)

simplify23.0ms (0.2%)

prune9.0ms (0.1%)

localize32.0ms (0.2%)

series62.0ms (0.4%)

rewrite39.0ms (0.3%)

simplify48.0ms (0.3%)

prune245.0ms (1.7%)

localize47.0ms (0.3%)

series80.0ms (0.6%)

rewrite34.0ms (0.2%)

simplify63.0ms (0.4%)

prune311.0ms (2.2%)

localize34.0ms (0.2%)

series1.3s (9.2%)

rewrite37.0ms (0.3%)

simplify50.0ms (0.4%)

prune401.0ms (2.8%)

localize29.0ms (0.2%)

series36.0ms (0.3%)

rewrite36.0ms (0.2%)

simplify37.0ms (0.3%)

prune340.0ms (2.4%)

regimes1.1s (8%)

simplify4.0ms (0%)

end369.0ms (2.6%)

Profiling