Details

analyze1.3s (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)

sample8.9s (57.6%)

Results

5.9s	3688×	body	1024	valid
1.5s	1381×	body	512	valid
813.0ms	2565×	body	128	valid
522.0ms	599×	body	256	valid
70.0ms	23×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify46.0ms (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)))
	0.4b	(/.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)

localize32.0ms (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))
✓	1.4b	(-.f64 (cos.f64 x) (cos.f64 y))

series23.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

16.0ms	(*.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)

rewrite56.0ms (0.4%)

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:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
6.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify250.0ms (1.6%)

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

prune1.0s (6.6%)

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
	0.4b	(/.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)))
	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)))
	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 (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 (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 (log.f64 (exp.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 (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)))
	0.6b	(/.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)))
▶	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)))
	0.8b	(/.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))) (-.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)))
	1.0b	(/.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 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.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 (+.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 22076 to 14265 computations (35.4% saved)

localize34.0ms (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)))

rewrite74.0ms (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:

39.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
8.0ms	(/.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 (7.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	308	10	318

Error

0.1b

Counts

318 → 10

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 (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 (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 (log.f64 (exp.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 (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)))
	0.6b	(/.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)))
✓	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 (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)))
	0.8b	(/.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))) (-.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)))
	1.0b	(/.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 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.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 (+.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 19877 to 14058 computations (29.3% 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)
	1.4b	(-.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)

simplify11.0ms (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

prune552.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	188	9	197

Error

0.1b

Counts

197 → 9

Alt Table

Status	Error	Program
▶	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) (.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 (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) (.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 (.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 1 (/.f64 2/3 (+.f64 -1 (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 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))
✓	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)))
	0.8b	(/.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))) (-.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.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 12652 to 8968 computations (29.1% saved)

localize37.0ms (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)
✓	1.4b	(+.f64 (cos.f64 x) (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))))

series10.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

3.0ms

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

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

545×	`fma-neg_binary64`
433×	`distribute-rgt-in_binary64`
310×	`neg-sub0_binary64`
299×	`neg-mul-1_binary64`
290×	`associate-l_binary64`

Counts

41 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	801
1	208	440
2	652	434
3	2252	434
4	4557	434
5	5036	434

prune518.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	177	9	186

Error

0.1b

Counts

186 → 9

Alt Table

Status	Error	Program
✓	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) (.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 (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) (.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 (.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 1 (/.f64 2/3 (+.f64 -1 (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 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))
✓	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)))
	0.8b	(/.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))) (-.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.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 13018 to 8198 computations (37% saved)

regimes857.0ms (5.5%)

Accuracy

Total 0.3b remaining (72.8%)

Threshold costs 0.3b (72.8%)

Counts

153 → 1

Compiler

Compiled 25796 to 19510 computations (24.4% 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

end342.0ms (2.2%)

Compiler: Compiled 601 to 463 computations (23% saved)

Details

analyze1.3s (8.4%)

sample8.9s (57.6%)

simplify46.0ms (0.3%)

prune7.0ms (0%)

localize32.0ms (0.2%)

series23.0ms (0.1%)

rewrite56.0ms (0.4%)

simplify250.0ms (1.6%)

prune1.0s (6.6%)

localize34.0ms (0.2%)

series0.0ms (0%)

rewrite74.0ms (0.5%)

simplify189.0ms (1.2%)

prune1.1s (7.1%)

localize33.0ms (0.2%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify11.0ms (0.1%)

prune552.0ms (3.6%)

localize37.0ms (0.2%)

series10.0ms (0.1%)

rewrite3.0ms (0%)

simplify66.0ms (0.4%)

prune518.0ms (3.3%)

regimes857.0ms (5.5%)

simplify5.0ms (0%)

end342.0ms (2.2%)

Profiling