Details

analyze354.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 37 to 28 computations (24.3% saved)

sample1.8s (38.4%)

Results

1.7s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 88 to 67 computations (23.9% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`sub-neg_binary32`
7×	`+-commutative_binary32`
6×	`fma-def_binary32`
4×	`*-commutative_binary32`
4×	`div-sub_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 42 to 33 computations (21.4% saved)

localize31.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
✓	0.1b	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.4b	(*.f32 314159265359/50000000000 u2)

series36.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

24.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
9.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
2.0ms	(/.f32 u1 (-.f32 1 u1))
2.0ms	(*.f32 314159265359/50000000000 u2)

rewrite68.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

532×	`log-prod_binary32`
271×	`prod-diff_binary32`
196×	`expm1-udef_binary32`
195×	`log1p-udef_binary32`
173×	`log-pow_binary32`

Counts

4 → 113

Calls

4 calls:

66.0ms	(sqrt.f32 (/.f32 u1 (-.f32 1 u1)))
66.0ms	(.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
66.0ms	(/.f32 u1 (-.f32 1 u1))
66.0ms	(*.f32 314159265359/50000000000 u2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	227	37
2	2724	37
3	5084	37
0	0	0
1	0	0

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-neg_binary32`
404×	`associate-/r*_binary32`
373×	`fma-def_binary32`
270×	`associate-+l+_binary32`
225×	`associate-+r+_binary32`

Counts

153 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	1248
1	343	1193
2	1136	1063
3	4658	1062
4	5154	1062

prune195.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	10	153
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Error

0.0b

Counts

154 → 10

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 3)) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.4b	(.f32 (/.f32 1 (sqrt.f32 (/.f32 (-.f32 1 u1) u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 2)
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 3)
	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	14.6b	(.f32 (sqrt.f32 (+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 u1 (-.f32 1 u1))))))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.3b	(/.f32 (.f32 (sqrt.f32 u1) (cos.f32 (.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
	0.4b	(.f32 (sqrt.f32 (.f32 (/.f32 1 (sqrt.f32 (-.f32 1 u1))) (/.f32 u1 (sqrt.f32 (-.f32 1 u1))))) (cos.f32 (*.f32 314159265359/50000000000 u2)))
	1.4b	(.f32 (pow.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) 1/3) (cos.f32 (.f32 314159265359/50000000000 u2)))
▶	0.3b	(cbrt.f32 (.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))

Compiler

Compiled 3313 to 2593 computations (21.7% saved)

localize43.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
✓	0.3b	(pow.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 3)
✓	0.3b	(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2)
	0.4b	(*.f32 314159265359/50000000000 u2)

series10.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

6.0ms	(pow.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 3)
4.0ms	(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2)

rewrite57.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

559×	`log-prod_binary32`
271×	`prod-diff_binary32`
222×	`expm1-udef_binary32`
221×	`log1p-udef_binary32`
192×	`log-pow_binary32`

Counts

2 → 45

Calls

2 calls:

56.0ms	(pow.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 3)
56.0ms	(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	276	19
2	3016	19
3	5424	19
0	0	0
1	0	0

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-neg_binary32`
777×	`cancel-sign-sub-inv_binary32`
538×	`times-frac_binary32`
434×	`fma-def_binary32`
385×	`unswap-sqr_binary32`

Counts

61 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	302
1	147	292
2	334	240
3	823	228
4	2319	228
5	5436	228

prune156.0ms (3.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Error

0.0b

Counts

150 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 3)) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 2)
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 3)
	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.3b	(/.f32 (.f32 (sqrt.f32 u1) (cos.f32 (.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
	0.4b	(cbrt.f32 (.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) (log.f32 (exp.f32 (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))))
▶	0.3b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)) (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))
	1.4b	(.f32 (pow.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) 1/3) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 3191 to 2591 computations (18.8% saved)

localize40.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 u1 (-.f32 1 u1))
	0.3b	(pow.f32 (cos.f32 (*.f32 314159265359/50000000000 u2)) 3)
	0.4b	(*.f32 314159265359/50000000000 u2)
✓	0.5b	(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)

rewrite95.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

730×	`log1p-expm1-u_binary32`
730×	`expm1-log1p-u_binary32`
150×	`prod-diff_binary32`
125×	`fma-udef_binary32`
123×	`log1p-udef_binary32`

Counts

1 → 36

Calls

1 calls:

94.0ms

(pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	154	10
2	1833	10
3	5000	10
4	4995	10
5	4904	10
0	0	0
1	0	0

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary32`
493×	`unswap-sqr_binary32`
419×	`fma-neg_binary32`
329×	`associate-l_binary32`
303×	`distribute-rgt-out_binary32`

Counts

48 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	174
1	103	160
2	303	156
3	820	156
4	2159	156
5	4764	156
6	4921	156
7	4983	156

prune161.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	154	8	162

Error

0.0b

Counts

162 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 3)) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 2)
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 3)
▶	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.3b	(/.f32 (.f32 (sqrt.f32 u1) (cos.f32 (.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
	0.4b	(cbrt.f32 (.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) (log.f32 (exp.f32 (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))))
✓	0.3b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)) (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))
	1.4b	(.f32 (pow.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) 1/3) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 3614 to 2941 computations (18.6% saved)

localize47.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1)))
✓	0.1b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
✓	0.3b	(.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))
	0.4b	(*.f32 314159265359/50000000000 u2)

series61.0ms (1.3%)

Counts

3 → 40

Calls

3 calls:

49.0ms

(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))

9.0ms

(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1)))

2.0ms

(*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))

rewrite70.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

798×	`prod-diff_binary32`
151×	`add-sqr-sqrt_binary32`
144×	`log1p-expm1-u_binary32`
144×	`expm1-log1p-u_binary32`
142×	`add-log-exp_binary32`

Counts

3 → 90

Calls

3 calls:

68.0ms

(sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1)))

68.0ms

(*.f32 (sqrt.f32 (*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (*.f32 314159265359/50000000000 u2)))

68.0ms

(*.f32 (/.f32 u1 (-.f32 1 (*.f32 u1 u1))) (+.f32 u1 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	306	33
2	3791	33
3	5272	33
0	0	0
1	0	0

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary32`
406×	`associate-/r*_binary32`
386×	`fma-def_binary32`
268×	`associate-+l+_binary32`
225×	`associate-+r+_binary32`

Counts

130 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1414
1	346	1291
2	1156	1154
3	4717	1152
4	5241	1152

prune116.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	144	8	152

Error

0.0b

Counts

152 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 u1 (-.f32 1 u1))) 3)) (cos.f32 (.f32 314159265359/50000000000 u2)))
	1.3b	(pow.f32 (sqrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 2)
	0.8b	(pow.f32 (cbrt.f32 (.f32 (sqrt.f32 (/.f32 u1 (-.f32 1 u1))) (cos.f32 (.f32 314159265359/50000000000 u2)))) 3)
✓	0.3b	(.f32 (sqrt.f32 (.f32 (/.f32 u1 (-.f32 1 (.f32 u1 u1))) (+.f32 u1 1))) (cos.f32 (.f32 314159265359/50000000000 u2)))
	0.3b	(/.f32 (.f32 (sqrt.f32 u1) (cos.f32 (.f32 314159265359/50000000000 u2))) (sqrt.f32 (-.f32 1 u1)))
	0.4b	(cbrt.f32 (.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) (log.f32 (exp.f32 (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))))
✓	0.3b	(cbrt.f32 (.f32 (sqrt.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3)) (pow.f32 (cos.f32 (.f32 314159265359/50000000000 u2)) 3)))
	1.4b	(.f32 (pow.f32 (pow.f32 (/.f32 u1 (-.f32 1 u1)) 3/2) 1/3) (cos.f32 (.f32 314159265359/50000000000 u2)))

Compiler

Compiled 3197 to 2313 computations (27.7% saved)

regimes938.0ms (20.4%)

Accuracy

Total 0.2b remaining (70%)

Threshold costs 0.2b (70%)

Counts

116 → 1

Compiler

Compiled 18247 to 14656 computations (19.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`
2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	18	18
2	22	18
3	24	18
4	25	18
5	24	18

end105.0ms (2.3%)

Compiler: Compiled 172 to 140 computations (18.6% saved)

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17

Details

analyze354.0ms (7.7%)

sample1.8s (38.4%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize31.0ms (0.7%)

series36.0ms (0.8%)

rewrite68.0ms (1.5%)

simplify64.0ms (1.4%)

prune195.0ms (4.2%)

localize43.0ms (0.9%)

series10.0ms (0.2%)

rewrite57.0ms (1.2%)

simplify38.0ms (0.8%)

prune156.0ms (3.4%)

localize40.0ms (0.9%)

series3.0ms (0.1%)

rewrite95.0ms (2.1%)

simplify69.0ms (1.5%)

prune161.0ms (3.5%)

localize47.0ms (1%)

series61.0ms (1.3%)

rewrite70.0ms (1.5%)

simplify63.0ms (1.4%)

prune116.0ms (2.5%)

regimes938.0ms (20.4%)

simplify2.0ms (0%)

end105.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	11	17
1	17	17
2	21	17
3	27	17
4	34	17
5	44	17
6	54	17
7	69	17
8	76	17
9	79	17
10	80	17
11	60	17