Details

analyze1.2s (17.7%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample2.9s (40.9%)

Symmetry

(sort c s)

Results

1.1s	6315×	body	128	valid
657.0ms	980×	body	1024	valid
336.0ms	1967×	body	128	invalid
266.0ms	611×	body	512	valid
140.0ms	210×	body	1024	invalid
121.0ms	268×	body	512	invalid
107.0ms	350×	body	256	valid
45.0ms	151×	body	256	invalid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

750×	`unswap-sqr_binary64`
516×	`*-commutative_binary64`
376×	`associate-/l/_binary64`
309×	`sqr-pow_binary64`
243×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	30	24
2	72	24
3	254	24
4	1145	24
5	2128	24
6	3320	24
7	3397	24
8	3494	24
9	3628	24
10	3813	24
11	4060	24
12	4401	24
13	4796	24

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

1.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	29.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
▶	1.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))

Compiler

Compiled 111 to 69 computations (37.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
✓	0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
✓	4.8b	(.f64 x (.f64 c s))

series165.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

121.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
33.0ms	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
10.0ms	(.f64 x (.f64 c s))

rewrite54.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`log-prod_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
205×	`prod-diff_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	236	35
2	3237	35

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

53.0ms	(.f64 (.f64 x (.f64 c s)) (.f64 x (*.f64 c s)))
53.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 x (.f64 c s))))
53.0ms	(.f64 x (.f64 c s))

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

866×	`associate-/l*_binary64`
440×	`associate-/l/_binary64`
361×	`cancel-sign-sub-inv_binary64`
334×	`unswap-sqr_binary64`
271×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	1776
1	111	1774
2	329	1774
3	1676	1769

Stop Event

1×	node limit

Counts

192 → 101

prune134.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	13	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Error

0.7b

Counts

126 → 13

Alt Table

Status	Error	Program
	1.7b	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))) 3)
▶	1.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))
	19.2b	(.f64 (/.f64 1 (.f64 (.f64 c s) (.f64 x x))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c s)))
	1.6b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)))
	31.0b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (pow.f64 (sqrt.f64 (.f64 x (.f64 c s))) 2)))
	1.8b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (pow.f64 (cbrt.f64 (.f64 x (.f64 c s))) 3)))
	15.0b	(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 s x) (.f64 (.f64 s x) (.f64 c c))))
	29.7b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) x) (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	4.2b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 s (.f64 c x))))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	1.4b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 x (*.f64 c s)) 2))))
	2.2b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (pow.f64 (cbrt.f64 (.f64 x (*.f64 c s))) 2) 3))
	22.4b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (pow.f64 (pow.f64 (.f64 x (*.f64 c s)) 2) 3) 1/3))

Compiler

Compiled 2977 to 1354 computations (54.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))
✓	0.3b	(pow.f64 (.f64 x (.f64 c s)) -2)
	4.8b	(.f64 x (.f64 c s))

series158.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

123.0ms	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))
35.0ms	(pow.f64 (.f64 x (.f64 c s)) -2)

rewrite43.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
147×	`fma-def_binary64`
124×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	241	28
2	3176	28

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

43.0ms	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))
43.0ms	(pow.f64 (.f64 x (.f64 c s)) -2)

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
437×	`associate-/l/_binary64`
361×	`cancel-sign-sub-inv_binary64`
355×	`unswap-sqr_binary64`
271×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	1632
1	99	1630
2	323	1630
3	1826	1625

Stop Event

1×	node limit

Counts

106 → 46

prune121.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	68	14	82

Error

0.0b

Counts

82 → 14

Alt Table

Status	Error	Program
	32.3b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (sqrt.f64 (.f64 s (.f64 x c))) -2) (pow.f64 (sqrt.f64 (.f64 s (.f64 x c))) -2)))
	29.7b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) x) (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	2.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	22.7b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 x -2) (pow.f64 (*.f64 c s) -2)))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 s (*.f64 c x)) -2))
▶	1.4b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 x (*.f64 c s)) 2))))
	31.0b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (pow.f64 (sqrt.f64 (.f64 x (.f64 c s))) 2)))
	15.0b	(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 s x) (.f64 (.f64 s x) (.f64 c c))))
	21.7b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (pow.f64 (*.f64 x c) -2) (pow.f64 s -2)))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (/.f64 1 (.f64 s (.f64 x c))) (/.f64 1 (.f64 s (.f64 x c)))))
	2.2b	(/.f64 (cos.f64 (.f64 2 x)) (pow.f64 (pow.f64 (cbrt.f64 (.f64 x (*.f64 c s))) 2) 3))
	1.7b	(pow.f64 (cbrt.f64 (.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (*.f64 c s)) -2))) 3)
	1.6b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)))

Compiler

Compiled 1787 to 891 computations (50.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 x (*.f64 c s)) 2))))
✓	0.2b	(pow.f64 (.f64 x (.f64 c s)) 2)
✓	0.3b	(/.f64 1 (neg.f64 (pow.f64 (.f64 x (.f64 c s)) 2)))
	4.8b	(.f64 x (.f64 c s))

series267.0ms (3.8%)

Counts

3 → 108

Calls

3 calls:

126.0ms	(/.f64 1 (neg.f64 (pow.f64 (.f64 x (.f64 c s)) 2)))
123.0ms	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 x (*.f64 c s)) 2))))
17.0ms	(pow.f64 (.f64 x (.f64 c s)) 2)

rewrite60.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`prod-diff_binary64`
155×	`add-sqr-sqrt_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`
145×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	323	41
2	4304	41

Stop Event

1×	node limit

Counts

3 → 101

Calls

3 calls:

58.0ms	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 x (*.f64 c s)) 2))))
58.0ms	(pow.f64 (.f64 x (.f64 c s)) 2)
58.0ms	(/.f64 1 (neg.f64 (pow.f64 (.f64 x (.f64 c s)) 2)))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

877×	`associate-/l*_binary64`
531×	`associate-/l/_binary64`
361×	`cancel-sign-sub-inv_binary64`
355×	`unswap-sqr_binary64`
283×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	2208
1	106	2206
2	348	2206
3	1952	2201

Stop Event

1×	node limit

Counts

209 → 118

prune207.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Error

0.0b

Counts

155 → 11

Alt Table

Status	Error	Program
	15.0b	(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 s x) (.f64 (.f64 s x) (.f64 c c))))
	7.5b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (.f64 (.f64 (.f64 x (.f64 c s)) (.f64 x c)) s))))
	29.7b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) x) (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	2.3b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 c (*.f64 s x)) 2))))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (/.f64 1 (.f64 s (.f64 x c))) (/.f64 1 (.f64 s (.f64 x c)))))
	1.8b	(pow.f64 (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (.f64 c s)) 2))) 3)
	5.0b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (.f64 x (.f64 (.f64 c s) (.f64 x (.f64 c s)))))))
	2.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 s (*.f64 c x)) -2))
▶	1.6b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)))

Compiler

Compiled 3267 to 1468 computations (55.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))
✓	0.3b	(pow.f64 (cos.f64 x) 2)
✓	3.6b	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))
	4.8b	(.f64 x (.f64 c s))

series267.0ms (3.8%)

Counts

3 → 76

Calls

3 calls:

134.0ms	(/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))
129.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))
3.0ms	(pow.f64 (cos.f64 x) 2)

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`expm1-udef_binary64`
246×	`log1p-udef_binary64`
232×	`log-pow_binary64`
140×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	295	36
2	3735	36

Stop Event

1×	node limit

Counts

3 → 92

Calls

3 calls:

60.0ms	(/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))
60.0ms	(pow.f64 (cos.f64 x) 2)
60.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

482×	`unswap-sqr_binary64`
473×	`times-frac_binary64`
454×	`fma-neg_binary64`
397×	`associate-/r*_binary64`
217×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	1929
1	188	1929
2	634	1925
3	3810	1925

Stop Event

1×	node limit

Counts

168 → 121

prune231.0ms (3.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	167	11	178

Error

0.0b

Counts

178 → 11

Alt Table

Status	Error	Program
	15.0b	(/.f64 (cos.f64 (.f64 x 2)) (.f64 (.f64 s x) (.f64 (.f64 s x) (.f64 c c))))
	7.5b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (.f64 (.f64 (.f64 x (.f64 c s)) (.f64 x c)) s))))
	29.7b	(.f64 (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) x) (/.f64 (sqrt.f64 (cos.f64 (+.f64 x x))) (.f64 (pow.f64 (*.f64 c s) 2) x)))
	2.3b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (pow.f64 (.f64 c (*.f64 s x)) 2))))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (.f64 (/.f64 1 (.f64 s (.f64 x c))) (/.f64 1 (.f64 s (.f64 x c)))))
	1.8b	(pow.f64 (cbrt.f64 (/.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 x (.f64 c s)) 2))) 3)
	5.0b	(.f64 (neg.f64 (cos.f64 (+.f64 x x))) (/.f64 1 (neg.f64 (.f64 x (.f64 (.f64 c s) (.f64 x (.f64 c s)))))))
	2.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 c (*.f64 s x)) -2))
	3.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (.f64 x (.f64 c s)) (.f64 c (.f64 s x))))
	3.3b	(.f64 (cos.f64 (+.f64 x x)) (pow.f64 (.f64 s (*.f64 c x)) -2))
✓	1.6b	(-.f64 (/.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (.f64 x (.f64 c s)) 2)))

Compiler

Compiled 5294 to 2490 computations (53% saved)

regimes641.0ms (9.2%)

Accuracy

Total 2.4b remaining (97.7%)

Threshold costs 0b (0%)

Counts

104 → 1

Compiler

Compiled 12748 to 8658 computations (32.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	14	18

Stop Event

1×

saturated

end163.0ms (2.3%)

Remove: (sort c s)
Compiler: Compiled 286 to 183 computations (36% saved)

Details

analyze1.2s (17.7%)

sample2.9s (40.9%)

simplify64.0ms (0.9%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series165.0ms (2.4%)

rewrite54.0ms (0.8%)

simplify46.0ms (0.7%)

prune134.0ms (1.9%)

localize8.0ms (0.1%)

series158.0ms (2.3%)

rewrite43.0ms (0.6%)

simplify44.0ms (0.6%)

prune121.0ms (1.7%)

localize11.0ms (0.2%)

series267.0ms (3.8%)

rewrite60.0ms (0.9%)

simplify55.0ms (0.8%)

prune207.0ms (3%)

localize14.0ms (0.2%)

series267.0ms (3.8%)

rewrite62.0ms (0.9%)

simplify56.0ms (0.8%)

prune231.0ms (3.3%)

regimes641.0ms (9.2%)

simplify2.0ms (0%)

end163.0ms (2.3%)

Profiling