Details

analyze10.0ms (0.3%)

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 (57.3%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify18.0ms (0.6%)

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)

localize16.0ms (0.5%)

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))

rewrite70.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

31× egg-rr

Counts

1 → 31

Calls

2 calls:

69.0ms	((fma.f32 ux maxCos (-.f32 1 ux)))
0.0ms	()

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 (0.8%)

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

prune26.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Error

0.0b

Counts

40 → 4

Alt Table

Status	Error	Program
	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))
▶	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 488 to 305 computations (37.5% saved)

localize15.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite96.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

98× egg-rr

Counts

1 → 98

Calls

2 calls:

94.0ms	((-.f32 (fma.f32 maxCos ux 1) ux))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1534	8
3	4984	8
4	4965	8
5	4971	8
0	0	0
1	0	0

simplify26.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

122 → 107

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

prune71.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	108	3	111

Error

0.0b

Counts

111 → 3

Alt Table

Status	Error	Program
	0.5b	(*.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (pow.f32 (cbrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) 2))
▶	0.1b	(fma.f32 (cbrt.f32 (*.f32 ux ux)) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 1584 to 826 computations (47.9% saved)

localize35.0ms (1.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f32 (cbrt.f32 (*.f32 ux ux)) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1))
✓	0.1b	(cbrt.f32 ux)
✓	0.1b	(cbrt.f32 (*.f32 ux ux))

series273.0ms (9.6%)

Counts

3 → 48

Calls

3 calls:

122.0ms	(fma.f32 (cbrt.f32 (*.f32 ux ux)) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1))
122.0ms	(cbrt.f32 (*.f32 ux ux))
29.0ms	(cbrt.f32 ux)

rewrite98.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

97× egg-rr

Counts

3 → 97

Calls

2 calls:

96.0ms	((cbrt.f32 (.f32 ux ux)) (cbrt.f32 ux) (fma.f32 (cbrt.f32 (.f32 ux ux)) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	188	15
2	1750	15
3	4925	15
4	4974	15
5	4961	15
0	0	0
1	0	0

simplify103.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

866×	`unswap-sqr_binary32`
699×	`fma-neg_binary32`
502×	`fma-def_binary32`
361×	`cancel-sign-sub-inv_binary32`
317×	`*-commutative_binary32`

Counts

145 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	349
1	51	313
2	87	313
3	173	310
4	367	310
5	906	310
6	1621	310
7	3070	310
8	4461	310
9	4781	310
10	4921	310
11	4822	310

prune63.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f32 (pow.f32 ux 2/3) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1))
▶	0.0b	(fma.f32 ux (+.f32 (cbrt.f32 -1) maxCos) 1)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 1530 to 810 computations (47.1% saved)

localize19.0ms (0.7%)

Local error

Found 1 expressions with local error:

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

series26.0ms (0.9%)

Counts

1 → 24

Calls

1 calls:

26.0ms

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

rewrite38.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

26× egg-rr

Counts

1 → 26

Calls

2 calls:

37.0ms	((fma.f32 ux (+.f32 (cbrt.f32 -1) maxCos) 1))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	140	8
2	1597	8
3	5059	8
0	0	0
1	0	0

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary32`
4×	`+-commutative_binary32`
3×	`*-commutative_binary32`
2×	`associate-+r+_binary32`
2×	`associate-+l+_binary32`

Counts

50 → 35

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	268
1	25	232
2	34	214
3	42	214
4	41	214

prune23.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f32 (pow.f32 ux 2/3) (neg.f32 (cbrt.f32 ux)) (fma.f32 maxCos ux 1))
✓	0.0b	(fma.f32 ux (+.f32 (cbrt.f32 -1) maxCos) 1)
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 389 to 290 computations (25.4% saved)

regimes102.0ms (3.6%)

Accuracy

Total 0.0b remaining (92.5%)

Threshold costs 0.0b (92.5%)

Counts

30 → 1

Compiler

Compiled 1432 to 1052 computations (26.5% saved)

simplify2.0ms (0.1%)

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	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end41.0ms (1.4%)

Compiler: Compiled 53 to 38 computations (28.3% 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

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

analyze10.0ms (0.3%)

sample1.6s (57.3%)

simplify18.0ms (0.6%)

prune3.0ms (0.1%)

localize16.0ms (0.5%)

series4.0ms (0.1%)

rewrite70.0ms (2.4%)

simplify23.0ms (0.8%)

prune26.0ms (0.9%)

localize15.0ms (0.5%)

series4.0ms (0.1%)

rewrite96.0ms (3.4%)

simplify26.0ms (0.9%)

prune71.0ms (2.5%)

localize35.0ms (1.2%)

series273.0ms (9.6%)

rewrite98.0ms (3.4%)

simplify103.0ms (3.6%)

prune63.0ms (2.2%)

localize19.0ms (0.7%)

series26.0ms (0.9%)

rewrite38.0ms (1.3%)

simplify11.0ms (0.4%)

prune23.0ms (0.8%)

regimes102.0ms (3.6%)

simplify2.0ms (0.1%)

end41.0ms (1.4%)

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

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