Details

analyze1.7s (10.3%)

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)

sample8.8s (52.9%)

Results

5.8s	3576×	body	1024	valid
1.4s	1400×	body	512	valid
929.0ms	2610×	body	128	valid
463.0ms	648×	body	256	valid
63.0ms	22×	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
	0.5b	(/.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) (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)))))

▶

0.4b

(/.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)))

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize34.0ms (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))
✓	2.5b	(-.f64 (cos.f64 x) (cos.f64 y))

series25.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

17.0ms	(*.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)

rewrite57.0ms (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:

18.0ms	(*.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))

simplify251.0ms (1.5%)

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

prune838.0ms (5.1%)

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
	0.4b	(/.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)))
	0.9b	(/.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (cbrt.f64 (sin.f64 x)) (neg.f64 (.f64 (/.f64 (sin.f64 y) 16) 1))) (sqrt.f64 2)) (.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 y) 16)) 1 (.f64 (/.f64 (sin.f64 y) 16) 1)) (sqrt.f64 2))) (-.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)))))
	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 (-.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 (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 (.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (cbrt.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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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 22000 to 14219 computations (35.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) (sin.f64 x))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.0b	(-.f64 3 (sqrt.f64 5))
	2.5b	(-.f64 (cos.f64 x) (cos.f64 y))

series4.0ms (0%)

Counts

1 → 4

Calls

1 calls:

4.0ms

(*.f64 (sqrt.f64 2) (sin.f64 x))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
4×	`sqrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 24

Calls

1 calls:

4.0ms

(*.f64 (sqrt.f64 2) (sin.f64 x))

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

925×	`fma-neg_binary64`
612×	`fma-def_binary64`
589×	`cancel-sign-sub-inv_binary64`
512×	`distribute-rgt-neg-in_binary64`
317×	`distribute-lft-neg-in_binary64`

Counts

28 → 32

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	388
1	136	364
2	386	352
3	948	336
4	1996	336
5	3355	336
6	4430	336
7	4945	336
8	4998	336
9	4875	336

prune668.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	204	9	213

Error

0.1b

Counts

213 → 9

Alt Table

Status	Error	Program
	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)))
	0.9b	(/.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) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.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 (-.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 (fma.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (cbrt.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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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 12730 to 8697 computations (31.7% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (sqrt.f64 2) (sin.f64 x))
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	2.5b	(fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y)))

series836.0ms (5%)

Counts

1 → 24

Calls

1 calls:

835.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

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

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
499×	`associate-l_binary64`
461×	`sub-neg_binary64`
428×	`associate-r_binary64`
399×	`cancel-sign-sub-inv_binary64`

Counts

34 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	54	395
1	126	366
2	369	366
3	1098	366
4	4385	366
5	5086	366

prune559.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	185	10	195

Error

0.1b

Counts

195 → 10

Alt Table

Status	Error	Program
	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)))
	0.9b	(/.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)))))
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (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)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.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 (-.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 (fma.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (cbrt.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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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 13072 to 8076 computations (38.2% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (sin.f64 x))
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	2.5b	(-.f64 (cos.f64 x) (cos.f64 y))

series174.0ms (1.1%)

Counts

1 → 12

Calls

1 calls:

174.0ms

(cbrt.f64 (sin.f64 x))

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 (sin.f64 x))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
532×	`cancel-sign-sub-inv_binary64`
467×	`log-prod_binary64`
268×	`sub-neg_binary64`
261×	`unswap-sqr_binary64`

Counts

25 → 24

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	221
1	97	215
2	215	213
3	527	211
4	1576	205
5	4017	205
6	4452	205
7	4998	205
8	4894	205

prune882.0ms (5.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	243	11	254

Error

0.1b

Counts

254 → 11

Alt Table

Status	Error	Program
	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)))
	30.2b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (.f64 (cbrt.f64 (sqrt.f64 (sin.f64 x))) (cbrt.f64 (sqrt.f64 (sin.f64 x))))) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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)))
	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 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (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)))
✓	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.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 (-.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 (fma.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (cbrt.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 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 -1/16 (.f64 (sin.f64 y) (sqrt.f64 2)))) (-.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 16747 to 10101 computations (39.7% saved)

regimes933.0ms (5.6%)

Accuracy

Total 0.3b remaining (71.9%)

Threshold costs 0.3b (71.9%)

Counts

134 → 1

Compiler

Compiled 23636 to 17551 computations (25.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	80
1	52	80
2	64	80
3	72	80
4	77	80
5	78	80
6	76	80

end413.0ms (2.5%)

Compiler: Compiled 739 to 548 computations (25.8% saved)

Details

analyze1.7s (10.3%)

sample8.8s (52.9%)

simplify46.0ms (0.3%)

prune7.0ms (0%)

localize34.0ms (0.2%)

series25.0ms (0.1%)

rewrite57.0ms (0.3%)

simplify251.0ms (1.5%)

prune838.0ms (5.1%)

localize30.0ms (0.2%)

series4.0ms (0%)

rewrite5.0ms (0%)

simplify108.0ms (0.7%)

prune668.0ms (4%)

localize41.0ms (0.2%)

series836.0ms (5%)

rewrite1.0ms (0%)

simplify62.0ms (0.4%)

prune559.0ms (3.4%)

localize34.0ms (0.2%)

series174.0ms (1.1%)

rewrite1.0ms (0%)

simplify81.0ms (0.5%)

prune882.0ms (5.3%)

regimes933.0ms (5.6%)

simplify5.0ms (0%)

end413.0ms (2.5%)

Profiling