Details

analyze5.0ms (0.2%)

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)

sample1.5s (52.4%)

Results

1.5s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify14.0ms (0.5%)

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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	8
2	35	8
3	72	8
4	167	8
5	361	8
6	618	8
7	765	8
8	797	8
9	802	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f32 (fma.f32 ux maxCos 1) ux)
▶	0.0b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

Compiler

Compiled 54 to 36 computations (33.3% saved)

localize15.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

4.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))
3.0ms	(*.f32 ux maxCos)

rewrite41.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary32`
836×	`expm1-log1p-u_binary32`
78×	`add-sqr-sqrt_binary32`
75×	`add-cbrt-cube_binary32`
72×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	155	12
2	2179	12

Stop Event

1×	node limit

Counts

2 → 54

Calls

2 calls:

40.0ms	(*.f32 ux maxCos)
40.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

simplify23.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	303
1	33	267
2	70	267
3	145	267
4	280	267
5	476	267
6	646	267
7	726	267
8	737	267

Stop Event

1×

saturated

Counts

102 → 62

prune43.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	3	64

Error

Counts

64 → 3

Alt Table

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

Compiler

Compiled 875 to 498 computations (43.1% saved)

localize13.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite32.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`log1p-expm1-u_binary32`
629×	`expm1-log1p-u_binary32`
276×	`log-prod_binary32`
120×	`expm1-udef_binary32`
120×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	138	8
2	1624	8

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

31.0ms

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

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Stop Event

1×

saturated

Counts

50 → 34

prune25.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Error

Counts

37 → 3

Alt Table

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

Compiler

Compiled 437 to 302 computations (30.9% saved)

localize13.0ms (0.4%)

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))

rewrite31.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1514	8

Stop Event

1×	node limit

Counts

1 → 31

Calls

1 calls:

31.0ms

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

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Stop Event

1×

saturated

Counts

55 → 39

prune24.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	39	3	42

Error

Counts

42 → 3

Alt Table

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

Compiler

Compiled 481 to 285 computations (40.7% saved)

localize40.0ms (1.4%)

Local error

Found 4 expressions with local error:

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

series143.0ms (4.9%)

Counts

4 → 96

Calls

4 calls:

106.0ms	(/.f32 (-.f32 1 (pow.f32 (-.f32 ux (.f32 ux maxCos)) 3)) (+.f32 1 (+.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (.f32 ux maxCos))) (-.f32 ux (*.f32 ux maxCos)))))
16.0ms	(+.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (.f32 ux maxCos))) (-.f32 ux (.f32 ux maxCos)))
13.0ms	(pow.f32 (-.f32 ux (*.f32 ux maxCos)) 3)
8.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (*.f32 ux maxCos)))

rewrite74.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`log1p-udef_binary32`
152×	`add-sqr-sqrt_binary32`
150×	`log1p-expm1-u_binary32`
150×	`expm1-log1p-u_binary32`
148×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	76
1	312	74
2	4643	74

Stop Event

1×	node limit

Counts

4 → 136

Calls

4 calls:

70.0ms	(+.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (.f32 ux maxCos))) (-.f32 ux (.f32 ux maxCos)))
70.0ms	(.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (*.f32 ux maxCos)))
70.0ms	(pow.f32 (-.f32 ux (*.f32 ux maxCos)) 3)
70.0ms	(/.f32 (-.f32 1 (pow.f32 (-.f32 ux (.f32 ux maxCos)) 3)) (+.f32 1 (+.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (-.f32 ux (.f32 ux maxCos))) (-.f32 ux (*.f32 ux maxCos)))))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

552×	`associate-+r+_binary32`
327×	`associate-+l+_binary32`
323×	`fma-def_binary32`
286×	`times-frac_binary32`
253×	`associate-/l*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	356	6170
1	1241	5406

Stop Event

1×	node limit

Counts

232 → 203

prune309.0ms (10.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	203	3	206

Error

Counts

206 → 3

Alt Table

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

Compiler

Compiled 11309 to 6334 computations (44% saved)

regimes383.0ms (13.1%)

Accuracy

Total 0.0b remaining (65.9%)

Threshold costs 0.0b (65.9%)

Counts

96 → 1

Compiler

Compiled 9346 to 5677 computations (39.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	10	8

Stop Event

1×

saturated

end41.0ms (1.4%)

Compiler: Compiled 68 to 41 computations (39.7% saved)

Iter	Nodes	Cost
0	14	303
1	33	267
2	70	267
3	145	267
4	280	267
5	476	267
6	646	267
7	726	267
8	737	267

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Iter	Nodes	Cost
0	14	303
1	33	267
2	70	267
3	145	267
4	280	267
5	476	267
6	646	267
7	726	267
8	737	267

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Details

analyze5.0ms (0.2%)

sample1.5s (52.4%)

simplify14.0ms (0.5%)

prune3.0ms (0.1%)

localize15.0ms (0.5%)

series7.0ms (0.2%)

rewrite41.0ms (1.4%)

simplify23.0ms (0.8%)

prune43.0ms (1.5%)

localize13.0ms (0.4%)

series4.0ms (0.1%)

rewrite32.0ms (1.1%)

simplify19.0ms (0.6%)

prune25.0ms (0.8%)

localize13.0ms (0.4%)

series4.0ms (0.1%)

rewrite31.0ms (1.1%)

simplify19.0ms (0.6%)

prune24.0ms (0.8%)

localize40.0ms (1.4%)

series143.0ms (4.9%)

rewrite74.0ms (2.5%)

simplify66.0ms (2.3%)

prune309.0ms (10.6%)

regimes383.0ms (13.1%)

simplify2.0ms (0.1%)

end41.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	14	303
1	33	267
2	70	267
3	145	267
4	280	267
5	476	267
6	646	267
7	726	267
8	737	267

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171

Iter	Nodes	Cost
0	14	207
1	33	171
2	70	171
3	145	171
4	280	171
5	476	171
6	646	171
7	726	171
8	737	171