Details

analyze2.5s (8.4%)

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
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)

sample391.0ms (1.3%)

Algorithm

1×

intervals

Results

278.0ms	122×	body	1024	valid
56.0ms	43×	body	512	valid
28.0ms	71×	body	128	valid
15.0ms	20×	body	256	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

770×	`neg-mul-1_binary64`
444×	`distribute-rgt-neg-out_binary64`
438×	`distribute-lft-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	74
2	201	74
3	626	73
4	2261	71
5	4460	71
6	5422	71

prune8.0ms (0%)

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 (.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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 (*.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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 295 to 218 computations (26.1% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series25.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

16.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))
0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)

rewrite66.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`add-sqr-sqrt_binary64`
154×	`*-un-lft-identity_binary64`
128×	`add-cube-cbrt_binary64`
106×	`times-frac_binary64`
105×	`prod-diff_binary64`

Counts

4 → 273

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
7.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify370.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

387×	`cancel-sign-sub-inv_binary64`
375×	`fma-neg_binary64`
336×	`associate-l_binary64`
316×	`associate-r_binary64`
280×	`*-commutative_binary64`

Counts

305 → 333

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	594	8679
1	1199	6233
2	3223	5425
3	4633	5425
4	4981	5425
5	4696	5425

prune1.9s (6.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	326	9	335

Error

0.1b

Counts

335 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (+.f64 1 (sqrt.f64 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.9b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
	1.4b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
▶	0.4b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.7b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.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 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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)))))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 21936 to 14191 computations (35.3% saved)

localize65.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
	1.0b	(-.f64 3 (sqrt.f64 5))
✓	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
	1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

series0.0ms (0%)

Counts

2 → 0

Calls

2 calls:

0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
0.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))

rewrite145.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-sqr-sqrt_binary64`
172×	`times-frac_binary64`
146×	`*-un-lft-identity_binary64`
141×	`sqrt-prod_binary64`
75×	`add-cube-cbrt_binary64`

Counts

2 → 233

Calls

2 calls:

70.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
20.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))

simplify280.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

633×	`times-frac_binary64`
528×	`cancel-sign-sub-inv_binary64`
496×	`associate-/l*_binary64`
318×	`sub-neg_binary64`
318×	`fma-def_binary64`

Counts

233 → 212

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	5163
1	375	4567
2	1216	4565
3	3122	4503
4	4095	4447
5	5281	4447

prune1.3s (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	308	9	317

Error

0.1b

Counts

317 → 9

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (+.f64 1 (sqrt.f64 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.7b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.9b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
	1.4b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.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 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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 19880 to 14049 computations (29.3% saved)

localize167.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
✓	1.4b	(fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))
✓	34.2b	(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

series4.6s (15.5%)

Counts

2 → 36

Calls

2 calls:

3.3s

(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

1.3s

(fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

1.0ms

(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

1.0ms

(fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))

simplify125.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
686×	`associate-l_binary64`
572×	`associate-r_binary64`
414×	`cancel-sign-sub-inv_binary64`
283×	`fma-neg_binary64`

Counts

56 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	523
1	152	458
2	433	411
3	1345	411
4	4407	411
5	4740	411
6	4866	411

prune525.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	170	9	179

Error

0.1b

Counts

179 → 9

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (+.f64 1 (sqrt.f64 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.9b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
	1.4b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
▶	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.7b	(/.f64 (fma.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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.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 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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 18017 to 8082 computations (55.1% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
✓	1.5b	(log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))

series708.0ms (2.4%)

Counts

1 → 8

Calls

1 calls:

707.0ms

(log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`log-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 27

Calls

1 calls:

7.0ms

(log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))

simplify113.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-neg_binary64`
381×	`sub-neg_binary64`
327×	`times-frac_binary64`
228×	`associate-+l+_binary64`
222×	`associate-r_binary64`

Counts

35 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	825
1	306	781
2	892	663
3	3967	657
4	5024	657

prune1.4s (4.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	319	0	319
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	319	9	328

Error

0.1b

Counts

328 → 9

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (+.f64 1 (sqrt.f64 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.9b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
	1.4b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.7b	(/.f64 (fma.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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.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)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 5) 3/2 -3/2))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.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 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 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 20904 to 14207 computations (32% saved)

regimes2.1s (7.1%)

Accuracy

Total 0.2b remaining (66.6%)

Threshold costs 0.2b (66.6%)

Counts

237 → 1

Compiler

Compiled 41906 to 31975 computations (23.7% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	95
1	64	95
2	84	95
3	98	95
4	108	95
5	111	95
6	108	95

end3.0ms (0%)

Compiler: Compiled 62 to 50 computations (19.4% saved)

sample12.9s (43.2%)

Algorithm

1×

intervals

Results

8.1s	3521×	body	1024	valid
1.9s	1376×	body	512	valid
1.1s	2517×	body	128	valid
516.0ms	565×	body	256	valid
91.0ms	21×	body	2048	valid

Compiler

Compiled 705 to 495 computations (29.8% saved)

Details

analyze2.5s (8.4%)

sample391.0ms (1.3%)

simplify59.0ms (0.2%)

prune8.0ms (0%)

localize35.0ms (0.1%)

series25.0ms (0.1%)

rewrite66.0ms (0.2%)

simplify370.0ms (1.2%)

prune1.9s (6.3%)

localize65.0ms (0.2%)

series0.0ms (0%)

rewrite145.0ms (0.5%)

simplify280.0ms (0.9%)

prune1.3s (4.2%)

localize167.0ms (0.6%)

series4.6s (15.5%)

rewrite4.0ms (0%)

simplify125.0ms (0.4%)

prune525.0ms (1.8%)

localize38.0ms (0.1%)

series708.0ms (2.4%)

rewrite11.0ms (0%)

simplify113.0ms (0.4%)

prune1.4s (4.7%)

regimes2.1s (7.1%)

simplify10.0ms (0%)

end3.0ms (0%)

sample12.9s (43.2%)

Profiling