Details

analyze640.0ms (2.4%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.4s (9%)

Results

1.0s	1397×	body	1024	valid
907.0ms	5855×	body	128	valid
280.0ms	649×	body	512	valid
107.0ms	353×	body	256	valid
4.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize9.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

series11.0ms (0%)

Counts

1 → 36

Calls

1 calls:

11.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

rewrite46.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

838×	`log1p-expm1-u_binary64`
838×	`expm1-log1p-u_binary64`
564×	`prod-diff_binary64`
88×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	167	12
2	2097	12
3	6179	12

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

44.0ms

(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

584×	`unsub-neg_binary64`
359×	`fma-def_binary64`
340×	`sub-neg_binary64`
339×	`distribute-rgt-neg-in_binary64`
305×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	399
1	68	397
2	184	394
3	525	392
4	1693	392
5	3059	392
6	4486	392
7	5042	392

Stop Event

1×	node limit

Counts

61 → 40

prune26.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

0.0b

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	32.3b	(pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

Compiler

Compiled 521 to 169 computations (67.6% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
✓	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

series19.5s (74%)

Counts

2 → 72

Calls

2 calls:

19.2s	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)
285.0ms	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))

rewrite53.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`prod-diff_binary64`
466×	`log-prod_binary64`
225×	`fma-def_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	214	26
2	2520	26
3	5331	26

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

52.0ms	(cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))
52.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))) 3)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

466×	`times-frac_binary64`
438×	`associate-r_binary64`
360×	`fma-def_binary64`
347×	`associate-/l*_binary64`
310×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	409	4648
1	1398	4340
2	5196	4340

Stop Event

1×	node limit

Counts

149 → 157

prune143.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	191	6	197
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	193	7	200

Error

0.0b

Counts

200 → 7

Alt Table

Status	Error	Program
	2.6b	(pow.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y))))) 2)) 3)
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (*.f64 z (sqrt.f64 (cos.f64 y))) (sqrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
▶	0.3b	(fma.f64 (*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	30.6b	(fma.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (.f64 z (cos.f64 y))) (+.f64 x (sin.f64 y)))
	32.1b	(fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))
	15.2b	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) (+.f64 x (sin.f64 y)))

Compiler

Compiled 7050 to 3679 computations (47.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
✓	0.1b	(*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2))
✓	0.3b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 y))

series1.7s (6.6%)

Counts

4 → 84

Calls

4 calls:

867.0ms	(fma.f64 (*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
616.0ms	(*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2))
122.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
118.0ms	(cbrt.f64 (cos.f64 y))

rewrite111.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`prod-diff_binary64`
414×	`fma-udef_binary64`
266×	`fma-def_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	247	38
2	2846	36
3	4758	36
4	4805	36
5	4921	36

Stop Event

1×	node limit

Counts

4 → 81

Calls

4 calls:

110.0ms	(fma.f64 (*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
110.0ms	(*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 2))
110.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
110.0ms	(cbrt.f64 (cos.f64 y))

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
351×	`distribute-rgt-neg-in_binary64`
342×	`distribute-lft-neg-in_binary64`
243×	`associate-+l-_binary64`
242×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	897
1	198	889
2	570	877
3	1889	877
4	4809	877
5	4948	877

Stop Event

1×	node limit

Counts

165 → 118

prune115.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	151	5	156

Error

0.0b

Counts

156 → 5

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 1/3) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	30.6b	(fma.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (.f64 z (cos.f64 y))) (+.f64 x (sin.f64 y)))
	0.3b	(fma.f64 (.f64 z (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2))) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))

Compiler

Compiled 2782 to 1095 computations (60.6% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2)))
✓	0.2b	(pow.f64 (cos.f64 y) 2)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
	0.3b	(cbrt.f64 (cos.f64 y))

series626.0ms (2.4%)

Counts

3 → 40

Calls

3 calls:

443.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2)))
179.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))
4.0ms	(pow.f64 (cos.f64 y) 2)

rewrite78.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
325×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	157	25
2	1608	25
3	4956	25
4	4954	25

Stop Event

1×	node limit

Counts

3 → 67

Calls

3 calls:

77.0ms	(*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2)))
77.0ms	(pow.f64 (cos.f64 y) 2)
77.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

654×	`cancel-sign-sub-inv_binary64`
591×	`distribute-rgt-neg-in_binary64`
508×	`sub-neg_binary64`
458×	`distribute-lft-neg-in_binary64`
432×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	455
1	131	443
2	386	436
3	1201	436
4	2666	436
5	4515	436
6	4917	436

Stop Event

1×	node limit

Counts

107 → 90

prune130.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Error

Counts

126 → 6

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 2))) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	15.6b	(fma.f64 (*.f64 z (pow.f64 (pow.f64 (cos.f64 y) 1/3) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
✓	0.1b	(fma.f64 z (cos.f64 y) (+.f64 x (sin.f64 y)))
	0.3b	(fma.f64 (*.f64 z (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 y) 2))))) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))
	30.6b	(fma.f64 (sqrt.f64 (.f64 z (cos.f64 y))) (sqrt.f64 (.f64 z (cos.f64 y))) (+.f64 x (sin.f64 y)))
	0.3b	(fma.f64 (.f64 z (pow.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 2))) 2)) (cbrt.f64 (cos.f64 y)) (+.f64 x (sin.f64 y)))

Compiler

Compiled 2515 to 1158 computations (54% saved)

regimes305.0ms (1.2%)

Accuracy

Total 0.0b remaining (46.6%)

Threshold costs 0.0b (46.6%)

Counts

71 → 1

Compiler

Compiled 4671 to 3185 computations (31.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

Stop Event

1×

saturated

end103.0ms (0.4%)

Compiler: Compiled 138 to 89 computations (35.5% saved)

Details

analyze640.0ms (2.4%)

sample2.4s (9%)

simplify6.0ms (0%)

prune3.0ms (0%)

localize9.0ms (0%)

series11.0ms (0%)

rewrite46.0ms (0.2%)

simplify79.0ms (0.3%)

prune26.0ms (0.1%)

localize10.0ms (0%)

series19.5s (74%)

rewrite53.0ms (0.2%)

simplify76.0ms (0.3%)

prune143.0ms (0.5%)

localize10.0ms (0%)

series1.7s (6.6%)

rewrite111.0ms (0.4%)

simplify65.0ms (0.2%)

prune115.0ms (0.4%)

localize11.0ms (0%)

series626.0ms (2.4%)

rewrite78.0ms (0.3%)

simplify67.0ms (0.3%)

prune130.0ms (0.5%)

regimes305.0ms (1.2%)

simplify2.0ms (0%)

end103.0ms (0.4%)

Profiling