Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0.1%	0%	99.9%	1

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.4s (9.2%)

Results

1.3s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-def_binary32`
155×	`fma-neg_binary32`
47×	`cancel-sign-sub-inv_binary32`
34×	`sub-neg_binary32`
26×	`unsub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	63	8
4	142	8
5	262	8
6	381	8
7	434	8
8	458	8
9	463	8
10	428	8

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

rewrite71.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

583×	`log1p-expm1-u_binary32`
583×	`expm1-log1p-u_binary32`
265×	`log-prod_binary32`
227×	`prod-diff_binary32`
110×	`expm1-udef_binary32`

Counts

1 → 31

Calls

1 calls:

70.0ms

(fma.f32 ux maxCos (-.f32 1 ux))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	123	8
2	1454	8
3	4960	8
4	4965	8
0	0	0
1	0	0

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

161×	`fma-def_binary32`
149×	`fma-neg_binary32`
26×	`associate--r+_binary32`
26×	`sub-neg_binary32`
24×	`distribute-rgt-in_binary32`

Counts

55 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

prune19.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	2	40

Error

0.0b

Counts

40 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

Compiler

Compiled 432 to 267 computations (38.2% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

series7.3s (47.6%)

Counts

2 → 48

Calls

2 calls:

7.3s	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)
24.0ms	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

rewrite43.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

740×	`log1p-expm1-u_binary32`
740×	`expm1-log1p-u_binary32`
216×	`prod-diff_binary32`
138×	`log1p-udef_binary32`
80×	`add-sqr-sqrt_binary32`

Counts

2 → 51

Calls

2 calls:

42.0ms	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
42.0ms	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	170	18
2	1874	18
3	5054	18
0	0	0
1	0	0

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

929×	`times-frac_binary32`
307×	`cancel-sign-sub-inv_binary32`
211×	`sub-neg_binary32`
183×	`fma-def_binary32`
170×	`fma-neg_binary32`

Counts

99 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	2816
1	706	2670
2	2524	2570
3	5065	2570

prune116.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	155	3	158

Error

0.0b

Counts

158 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.3b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))
✓	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

Compiler

Compiled 4206 to 2825 computations (32.8% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.2b	(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)
✓	0.2b	(*.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3))
✓	0.2b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))

series383.0ms (2.5%)

Counts

3 → 72

Calls

3 calls:

355.0ms

(*.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3))

22.0ms

(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)

5.0ms

(*.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (*.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))

rewrite93.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

504×	`log-prod_binary32`
226×	`prod-diff_binary32`
189×	`expm1-udef_binary32`
188×	`log1p-udef_binary32`
177×	`pow3_binary32`

Counts

3 → 89

Calls

3 calls:

91.0ms

(pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)

91.0ms

(*.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3))

91.0ms

(*.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (*.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	76
1	258	43
2	2562	43
3	4879	43
4	4898	43
0	0	0
1	0	0

simplify203.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

424×	`*-commutative_binary32`
358×	`+-commutative_binary32`
336×	`fma-def_binary32`
308×	`associate-+r+_binary32`
166×	`associate-*r/_binary32`

Counts

161 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1153	15291
1	4383	14884
2	5068	14884

prune820.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	323	1	324
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	323	4	327

Error

Counts

327 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.7b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (-.f32 (fma.f32 7/9 (.f32 (.f32 maxCos ux) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)) (fma.f32 35/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 5))) (fma.f32 35/3 (.f32 (.f32 maxCos (pow.f32 ux 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)) (+.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 7) 1/9) (.f32 7/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 7)))))))) (fma.f32 14/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 6))) (fma.f32 140/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 4))) (.f32 14/3 (.f32 (.f32 maxCos (.f32 ux ux)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)))))))
✓	0.3b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))
✓	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

Compiler

Compiled 31763 to 23693 computations (25.4% saved)

localize211.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f32 14/3 (.f32 (.f32 maxCos (.f32 ux ux)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)))
✓	0.5b	(pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)
✓	1.0b	(pow.f32 (-.f32 1 ux) 7)
✓	2.8b	(pow.f32 (-.f32 1 ux) 56)

series414.0ms (2.7%)

Counts

4 → 60

Calls

4 calls:

402.0ms	(.f32 14/3 (.f32 (.f32 maxCos (.f32 ux ux)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)))
5.0ms	(pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)
4.0ms	(pow.f32 (-.f32 1 ux) 7)
3.0ms	(pow.f32 (-.f32 1 ux) 56)

rewrite64.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

300×	`log1p-udef_binary32`
220×	`prod-diff_binary32`
177×	`add-sqr-sqrt_binary32`
172×	`log1p-expm1-u_binary32`
172×	`expm1-log1p-u_binary32`

Counts

4 → 67

Calls

4 calls:

63.0ms	(.f32 14/3 (.f32 (.f32 maxCos (.f32 ux ux)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)))
63.0ms	(pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)
63.0ms	(pow.f32 (-.f32 1 ux) 7)
63.0ms	(pow.f32 (-.f32 1 ux) 56)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	377	40
2	4113	40
3	4745	40
0	0	0
1	0	0

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-neg_binary32`
629×	`fma-def_binary32`
577×	`cancel-sign-sub-inv_binary32`
292×	`associate-l_binary32`
284×	`distribute-lft-out_binary32`

Counts

127 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1353
1	401	1345
2	1066	1312
3	2874	1288
4	4906	1286
5	5025	1286

prune2.1s (13.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	514	0	514
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	514	4	518

Error

Counts

518 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.7b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (-.f32 (fma.f32 7/9 (.f32 (.f32 maxCos ux) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)) (fma.f32 35/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 5))) (fma.f32 35/3 (.f32 (.f32 maxCos (pow.f32 ux 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)) (+.f32 (pow.f32 (pow.f32 (-.f32 1 ux) 7) 1/9) (.f32 7/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 7)))))))) (fma.f32 14/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 6))) (fma.f32 140/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9) (.f32 maxCos (pow.f32 ux 4))) (.f32 14/3 (.f32 (.f32 maxCos (.f32 ux ux)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 1 ux) 56)) 1/9)))))))
✓	0.3b	(.f32 (cbrt.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)) (.f32 (cbrt.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))) (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 2/3)))
✓	0.5b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 3)

Compiler

Compiled 72296 to 56964 computations (21.2% saved)

regimes1.7s (11%)

Accuracy

Total 0.0b remaining (51.9%)

Threshold costs 0.0b (51.9%)

Counts

125 → 1

Compiler

Compiled 56685 to 45700 computations (19.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	14	8
3	16	8
4	17	8
5	16	8

end121.0ms (0.8%)

Compiler: Compiled 208 to 161 computations (22.6% saved)

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171

Details

analyze5.0ms (0%)

sample1.4s (9.2%)

simplify17.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series4.0ms (0%)

rewrite71.0ms (0.5%)

simplify23.0ms (0.1%)

prune19.0ms (0.1%)

localize21.0ms (0.1%)

series7.3s (47.6%)

rewrite43.0ms (0.3%)

simplify77.0ms (0.5%)

prune116.0ms (0.8%)

localize40.0ms (0.3%)

series383.0ms (2.5%)

rewrite93.0ms (0.6%)

simplify203.0ms (1.3%)

prune820.0ms (5.3%)

localize211.0ms (1.4%)

series414.0ms (2.7%)

rewrite64.0ms (0.4%)

simplify79.0ms (0.5%)

prune2.1s (13.8%)

regimes1.7s (11%)

simplify2.0ms (0%)

end121.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	14	207
1	33	171
2	69	171
3	120	171
4	206	171
5	332	171
6	438	171
7	446	171
8	457	171
9	422	171