Details

analyze1.1s (5%)

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)

sample12.2s (53.9%)

Infinites

0% of outputs are infinite.

Results

8.0s	3591×	body	1024	valid
2.2s	1423×	body	512	valid
1.3s	2657×	body	128	valid
586.0ms	566×	body	256	valid
81.0ms	19×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify55.0ms (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

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

0.4b

Counts

3 → 2

Alt Table

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

Status

Error

Program

0.5b

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

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize32.0ms (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))
✓	1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

series25.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

18.0ms	(*.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 (-.f64 (sqrt.f64 5) 1) 2/3)
0.0ms	(-.f64 3 (sqrt.f64 5))

rewrite62.0ms (0.3%)

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:

12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify450.0ms (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

prune1.5s (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	322	11	333
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	324	11	335

Error

0.1b

Counts

335 → 11

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 (.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)))
	0.5b	(/.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 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) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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)))
	0.6b	(/.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 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 (fma.f64 1 (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)))
	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 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 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (cbrt.f64 (.f64 (.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (-.f64 (cos.f64 x) (cos.f64 y))) (-.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)))
	1.2b	(/.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))) (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)))
	0.5b	(/.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 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))

Compiler

Compiled 22202 to 14335 computations (35.4% saved)

localize60.0ms (0.3%)

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)
	1.7b	(-.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)

simplify10.0ms (0%)

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

prune1.1s (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	188	10	198

Error

0.1b

Counts

198 → 10

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 (.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)))
	0.5b	(/.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 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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)))
	1.2b	(/.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))) (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)))
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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)))
	0.6b	(/.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 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)))
	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 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 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.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) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 12650 to 8906 computations (29.6% saved)

localize89.0ms (0.4%)

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)
✓	1.9b	(log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))

series850.0ms (3.7%)

Counts

1 → 8

Calls

1 calls:

850.0ms

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

rewrite8.0ms (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:

6.0ms

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

simplify67.0ms (0.3%)

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

prune692.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	198	10	208

Error

0.1b

Counts

208 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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)))
	1.2b	(/.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))) (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)))
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (/.f64 1 (.f64 (cbrt.f64 (exp.f64 (cos.f64 y))) (cbrt.f64 (exp.f64 (cos.f64 y)))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (cbrt.f64 (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)))
	0.6b	(/.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 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)))
	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 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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) (sqrt.f64 (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)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (sqrt.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))) (log.f64 (sqrt.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)))
▶	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (sqrt.f64 (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)))

Compiler

Compiled 13857 to 9480 computations (31.6% saved)

localize47.0ms (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)
✓	1.7b	(+.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (sqrt.f64 (exp.f64 (cos.f64 y))))))

series1.0s (4.6%)

Counts

1 → 24

Calls

1 calls:

1.0s	(+.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (sqrt.f64 (exp.f64 (cos.f64 y))))))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`log-prod_binary64`
36×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`

Counts

1 → 75

Calls

1 calls:

14.0ms

(+.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (sqrt.f64 (exp.f64 (cos.f64 y))))))

simplify135.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
734×	`fma-def_binary64`
319×	`associate--l+_binary64`
231×	`associate--r+_binary64`
173×	`associate-r_binary64`

Counts

99 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	3078
1	497	2659
2	1565	2272
3	4277	2266
4	4992	2266
5	4893	2266

prune1.2s (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	263	10	273

Error

0.1b

Counts

273 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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)))
	1.2b	(/.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))) (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)))
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (/.f64 1 (.f64 (cbrt.f64 (exp.f64 (cos.f64 y))) (cbrt.f64 (exp.f64 (cos.f64 y)))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (cbrt.f64 (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)))
	0.6b	(/.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 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)))
	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 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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (cbrt.f64 (exp.f64 (cos.f64 x))) (sqrt.f64 (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)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.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) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (sqrt.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.f64 (cos.f64 y))))) (log.f64 (sqrt.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)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 (cos.f64 y))))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (sqrt.f64 (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)))

Compiler

Compiled 20071 to 12722 computations (36.6% saved)

regimes1.3s (5.8%)

Accuracy

Total 0.3b remaining (71.9%)

Threshold costs 0.3b (71.9%)

Counts

189 → 1

Compiler

Compiled 33029 to 25024 computations (24.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	101
1	64	99
2	83	99
3	97	99
4	105	99
5	107	99
6	104	99

end578.0ms (2.5%)

Compiler: Compiled 737 to 558 computations (24.3% saved)

Details

analyze1.1s (5%)

sample12.2s (53.9%)

simplify55.0ms (0.2%)

prune7.0ms (0%)

localize32.0ms (0.1%)

series25.0ms (0.1%)

rewrite62.0ms (0.3%)

simplify450.0ms (2%)

prune1.5s (6.5%)

localize60.0ms (0.3%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify10.0ms (0%)

prune1.1s (4.8%)

localize89.0ms (0.4%)

series850.0ms (3.7%)

rewrite8.0ms (0%)

simplify67.0ms (0.3%)

prune692.0ms (3.1%)

localize47.0ms (0.2%)

series1.0s (4.6%)

rewrite26.0ms (0.1%)

simplify135.0ms (0.6%)

prune1.2s (5.3%)

regimes1.3s (5.8%)

simplify6.0ms (0%)

end578.0ms (2.5%)

Profiling