Details

analyze1.2s (7.8%)

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)

sample304.0ms (1.9%)

Algorithm

1×

intervals

Results

178.0ms	120×	body	1024	valid
37.0ms	42×	body	512	valid
19.0ms	77×	body	128	valid
9.0ms	17×	body	256	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify48.0ms (0.3%)

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

prune7.0ms (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)))
	0.5b	(/.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

▶

0.4b

(/.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)))

0.5b

(/.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 295 to 218 computations (26.1% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.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))
✓	2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

series35.0ms (0.2%)

Counts

4 → 32

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))
0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)

rewrite419.0ms (2.7%)

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:

202.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify275.0ms (1.8%)

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

prune846.0ms (5.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	324	9	333
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	325	10	335

Error

0.1b

Counts

335 → 10

Alt Table

Status	Error	Program
	0.6b	(/.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 (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)))
	0.6b	(/.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 (fma.f64 (sqrt.f64 3) (sqrt.f64 3) (neg.f64 (sqrt.f64 5)))) 3)))
	14.8b	(/.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))) (fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (neg.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)))
	0.9b	(/.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 (cbrt.f64 (+.f64 -1 (sqrt.f64 5))) (cbrt.f64 (+.f64 -1 (sqrt.f64 5)))) (/.f64 (cbrt.f64 (+.f64 -1 (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)))
	0.5b	(/.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)))))
	24.7b	(/.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 (sqrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (sqrt.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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3)))) (.f64 (sqrt.f64 2) 0)) (-.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)))

Compiler

Compiled 22052 to 14289 computations (35.2% saved)

localize37.0ms (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))
	2.1b	(-.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)))

rewrite67.0ms (0.4%)

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:

33.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
7.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))

simplify189.0ms (1.2%)

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

prune1.1s (7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	307	11	318

Error

0.1b

Counts

318 → 11

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 2/3)) (.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 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 (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)))
	0.4b	(/.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) (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (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)))
	24.7b	(/.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 (sqrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (sqrt.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)))
	0.6b	(/.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)))
	1.0b	(/.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 1 (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	14.8b	(/.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))) (fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (neg.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)))
	0.9b	(/.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)))
	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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3)))) (.f64 (sqrt.f64 2) 0)) (-.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)))
	1.0b	(/.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 1 (sqrt.f64 (sqrt.f64 5))) (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 5)) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 19983 to 14176 computations (29.1% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 3 (sqrt.f64 5))
✓	1.0b	(cbrt.f64 16)
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(cbrt.f64 16)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 16)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`associate-l_binary64`
1×	`rem-3cbrt-lft_binary64`
1×	`1-exp_binary64`

Counts

13 → 15

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	73
1	21	73
2	16	73

prune692.0ms (4.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	187	11	198

Error

0.1b

Counts

198 → 11

Alt Table

Status	Error	Program
	14.8b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3)))) (.f64 (sqrt.f64 2) 0)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (neg.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)))
	0.6b	(/.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)))
	0.5b	(/.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 2/3)) (.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 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 (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)))
	9.8b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3)))) (.f64 (sqrt.f64 2) 0)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (expm1.f64 (log1p.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)))
	1.0b	(/.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 1 (sqrt.f64 (sqrt.f64 5))) (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 5)) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	1.0b	(/.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 1 (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (cbrt.f64 (sqrt.f64 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)))
	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 (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) (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (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)))
▶	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (cbrt.f64 (cbrt.f64 16))) 3)))) (.f64 (sqrt.f64 2) 0)) (-.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)))

Compiler

Compiled 12934 to 9196 computations (28.9% saved)

localize108.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(cbrt.f64 16)
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	1.0b	(cbrt.f64 (cbrt.f64 16))
	2.1b	(-.f64 (cos.f64 x) (cos.f64 y))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(cbrt.f64 (cbrt.f64 16))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 16

Calls

1 calls:

1.0ms

(cbrt.f64 (cbrt.f64 16))

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

501×	`associate-l_binary64`
486×	`sqr-pow_binary64`
460×	`associate-/l/_binary64`
347×	`associate-/r/_binary64`
330×	`distribute-rgt-out_binary64`

Counts

16 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	146
1	28	146
2	41	146
3	52	142
4	80	138
5	138	138
6	284	138
7	888	138
8	955	138
9	1163	138
10	1565	138
11	2613	138
12	3313	138
13	4930	138
14	4747	138

prune714.0ms (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	191	11	202

Error

0.1b

Counts

202 → 11

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 2/3)) (.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 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 (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)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 16))) (sqrt.f64 (cbrt.f64 (cbrt.f64 16))))) 3)))) (.f64 (sqrt.f64 2) 0)) (-.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)))
	0.9b	(/.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)))
	9.8b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (cbrt.f64 (cbrt.f64 16))) 3)))) (.f64 (sqrt.f64 2) 0)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (expm1.f64 (log1p.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 (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) (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (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)))
	14.8b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) (pow.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (cbrt.f64 (cbrt.f64 16))) 3)))) (.f64 (sqrt.f64 2) 0)) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (sqrt.f64 (cos.f64 x)) (sqrt.f64 (cos.f64 x)) (neg.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)))
	1.0b	(/.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 1 (sqrt.f64 (sqrt.f64 5))) (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 (sqrt.f64 5)) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))
	1.0b	(/.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 1 (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (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)))))

Compiler

Compiled 13733 to 10056 computations (26.8% saved)

regimes1.5s (9.5%)

Accuracy

Total 0.3b remaining (73.8%)

Threshold costs 0.3b (73.8%)

Counts

220 → 1

Compiler

Compiled 37526 to 29041 computations (22.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	81
1	51	81
2	68	81
3	80	81
4	88	81
5	90	81
6	88	81

end1.0ms (0%)

Compiler: Compiled 53 to 41 computations (22.6% saved)

sample8.0s (50.7%)

Algorithm

1×

intervals

Results

4.9s	3453×	body	1024	valid
1.2s	1389×	body	512	valid
759.0ms	2510×	body	128	valid
350.0ms	637×	body	256	valid
30.0ms	11×	body	2048	valid

Compiler

Compiled 766 to 601 computations (21.5% saved)

Details

analyze1.2s (7.8%)

sample304.0ms (1.9%)

simplify48.0ms (0.3%)

prune7.0ms (0%)

localize30.0ms (0.2%)

series35.0ms (0.2%)

rewrite419.0ms (2.7%)

simplify275.0ms (1.8%)

prune846.0ms (5.4%)

localize37.0ms (0.2%)

series0.0ms (0%)

rewrite67.0ms (0.4%)

simplify189.0ms (1.2%)

prune1.1s (7%)

localize33.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify13.0ms (0.1%)

prune692.0ms (4.4%)

localize108.0ms (0.7%)

series0.0ms (0%)

rewrite2.0ms (0%)

simplify96.0ms (0.6%)

prune714.0ms (4.6%)

regimes1.5s (9.5%)

simplify5.0ms (0%)

end1.0ms (0%)

sample8.0s (50.7%)

Profiling