Details

analyze6.0ms (0.1%)

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)

sample1.6s (32.3%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify19.0ms (0.4%)

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 (0.1%)

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 (0.3%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite84.0ms (1.7%)

Algorithm

1×	egg-rewrite

Rules

48× egg

Counts

1 → 48

Calls

1 calls:

83.0ms

(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

simplify26.0ms (0.5%)

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

72 → 56

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

prune37.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

0.0b

Counts

57 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))

Compiler

Compiled 684 to 403 computations (41.1% saved)

localize39.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (fma.f32 ux ux ux))
✓	0.0b	(-.f32 1 (pow.f32 ux 3))
✓	0.1b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.4b	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))

series42.0ms (0.8%)

Counts

4 → 51

Calls

4 calls:

32.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
3.0ms	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))
3.0ms	(+.f32 1 (fma.f32 ux ux ux))
3.0ms	(-.f32 1 (pow.f32 ux 3))

rewrite311.0ms (6.2%)

Algorithm

4×	egg-rewrite

Rules

59×	`egg`
48×	`egg`
32×	`egg`
24×	`egg`

Counts

4 → 163

Calls

4 calls:

108.0ms	(-.f32 1 (pow.f32 ux 3))
88.0ms	(+.f32 1 (fma.f32 ux ux ux))
61.0ms	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
51.0ms	(/.f32 1 (+.f32 1 (fma.f32 ux ux ux)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	128	11
2	1510	11
3	5108	11
0	12	24
1	261	23
2	3085	23
3	5044	23
0	6	7
1	127	7
2	1356	7
3	4857	7
4	4922	7
5	5049	7
0	5	8
1	102	8
2	1194	8
3	4846	8
4	6340	8

simplify167.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary32`
493×	`unswap-sqr_binary32`
336×	`div-sub_binary32`
279×	`fma-def_binary32`
271×	`associate-l_binary32`

Counts

214 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	772
1	119	680
2	302	680
3	730	678
4	2202	678
5	4568	678
6	4975	678

prune144.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
	1.2b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))))) (cbrt.f32 (exp.f32 (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))))))) (log.f32 (cbrt.f32 (exp.f32 (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))))))) (.f32 ux maxCos))
▶	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))

Compiler

Compiled 4547 to 2675 computations (41.2% saved)

localize28.0ms (0.6%)

Local error

Found 4 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)))
✓	0.2b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))
✓	0.4b	(pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2)

series104.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

67.0ms

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

32.0ms

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

5.0ms

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

rewrite233.0ms (4.7%)

Algorithm

3×	egg-rewrite

Rules

33×	`egg`
23×	`egg`
19×	`egg`

Counts

3 → 75

Calls

3 calls:

138.0ms

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

47.0ms

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

46.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	183	11
2	1931	11
3	4959	11
0	10	8
1	186	8
2	1943	8
3	4987	8
0	7	10
1	140	10
2	1638	10
3	4823	10
4	4943	10
5	4985	10
6	4937	10

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

378×	`sub-neg_binary32`
368×	`fma-def_binary32`
299×	`fma-neg_binary32`
247×	`+-commutative_binary32`
233×	`associate-/r*_binary32`

Counts

147 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	4211
1	1161	3999
2	4309	3869
3	5105	3869

prune390.0ms (7.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	350	1	351
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	351	4	355

Error

Counts

355 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.7b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2))
✓	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))

Compiler

Compiled 13012 to 8600 computations (33.9% saved)

localize81.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.2b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2))
✓	0.4b	(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2)
✓	0.4b	(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2)

series244.0ms (4.9%)

Counts

3 → 72

Calls

3 calls:

172.0ms

(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2)

66.0ms

(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2)

5.0ms

(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2))

rewrite166.0ms (3.3%)

Algorithm

3×	egg-rewrite

Rules

34×	`egg`
28×	`egg`
26×	`egg`

Counts

3 → 88

Calls

3 calls:

58.0ms

(pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2)

54.0ms

(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2))

51.0ms

(pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	237	11
2	2314	11
3	5777	11
0	10	11
1	215	10
2	2160	10
3	5446	10
0	13	8
1	237	8
2	2329	8
3	5811	8

simplify337.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-def_binary32`
311×	`fma-neg_binary32`
244×	`+-commutative_binary32`
233×	`associate-/r*_binary32`
211×	`associate-r_binary32`

Counts

160 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	4383
1	1169	4176
2	4513	4166
3	5032	4166

prune552.0ms (11.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	249	4	253

Error

Counts

253 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.7b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (pow.f32 (pow.f32 (fma.f32 ux maxCos (-.f32 1 ux)) 1/6) 2) 2))
✓	0.4b	(fma.f32 (-.f32 1 (pow.f32 ux 3)) (/.f32 1 (+.f32 1 (fma.f32 ux ux ux))) (*.f32 ux maxCos))
✓	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))

Compiler

Compiled 11373 to 7857 computations (30.9% saved)

regimes159.0ms (3.2%)

Accuracy

Total 0.0b remaining (72%)

Threshold costs 0.0b (72%)

Counts

36 → 1

Compiler

Compiled 2494 to 1829 computations (26.7% saved)

simplify3.0ms (0.1%)

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

end62.0ms (1.2%)

Compiler: Compiled 90 to 63 computations (30% 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

analyze6.0ms (0.1%)

sample1.6s (32.3%)

simplify19.0ms (0.4%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

series4.0ms (0.1%)

rewrite84.0ms (1.7%)

simplify26.0ms (0.5%)

prune37.0ms (0.7%)

localize39.0ms (0.8%)

series42.0ms (0.8%)

rewrite311.0ms (6.2%)

simplify167.0ms (3.3%)

prune144.0ms (2.9%)

localize28.0ms (0.6%)

series104.0ms (2.1%)

rewrite233.0ms (4.7%)

simplify121.0ms (2.4%)

prune390.0ms (7.8%)

localize81.0ms (1.6%)

series244.0ms (4.9%)

rewrite166.0ms (3.3%)

simplify337.0ms (6.8%)

prune552.0ms (11.1%)

regimes159.0ms (3.2%)

simplify3.0ms (0.1%)

end62.0ms (1.2%)

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