Details

analyze4.0ms (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 (69.3%)

Results

1.4s	8254×	body	128	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 66 to 48 computations (27.3% saved)

preprocess41.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

601×	`fma-def_binary32`
498×	`fma-neg_binary32`
174×	`cancel-sign-sub-inv_binary32`
94×	`sub-neg_binary32`
89×	`unsub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	40	32
2	106	32
3	222	32
4	540	32
5	1153	32
6	1987	32
7	2325	32
8	2405	32
9	2416	32
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 7 computations (30% saved)

simplify15.0ms (0.7%)

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 (-.f32 1 ux) (*.f32 ux maxCos))
	0.1b	(-.f32 (fma.f32 ux maxCos 1) ux)

Compiler

Compiled 54 to 36 computations (33.3% saved)

localize14.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 ux maxCos)
✓	0.1b	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))

series7.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))	ux	-inf
1.0ms	(*.f32 ux maxCos)	maxCos	-inf
1.0ms	(*.f32 ux maxCos)	ux	-inf
1.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))	ux	inf
1.0ms	(+.f32 (-.f32 1 ux) (*.f32 ux maxCos))	ux	0

rewrite43.0ms (2%)

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

simplify22.0ms (1.1%)

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

prune41.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Error

Counts

64 → 2

Alt Table

Status	Error	Program
	0.6b	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))
▶	0.0b	(fma.f32 ux (+.f32 maxCos -1) 1)

Compiler

Compiled 827 to 484 computations (41.5% saved)

localize12.0ms (0.6%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f32 ux (+.f32 maxCos -1) 1)	ux	-inf
1.0ms	(fma.f32 ux (+.f32 maxCos -1) 1)	maxCos	-inf
1.0ms	(fma.f32 ux (+.f32 maxCos -1) 1)	ux	inf
1.0ms	(fma.f32 ux (+.f32 maxCos -1) 1)	ux	0
1.0ms	(fma.f32 ux (+.f32 maxCos -1) 1)	maxCos	inf

rewrite32.0ms (1.5%)

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

simplify19.0ms (0.9%)

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

prune20.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	34	2	36

Error

Counts

36 → 2

Alt Table

Status	Error	Program
▶	0.6b	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))
✓	0.0b	(fma.f32 ux (+.f32 maxCos -1) 1)

Compiler

Compiled 389 to 288 computations (26% saved)

localize26.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f32 ux maxCos)
✓	0.1b	(cbrt.f32 (-.f32 1 ux))
✓	0.2b	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))
✓	0.4b	(pow.f32 (cbrt.f32 (-.f32 1 ux)) 2)

series67.0ms (3.2%)

Counts

3 → 26

Calls

12 calls:

19.0ms	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))	maxCos	0
16.0ms	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))	maxCos	-inf
15.0ms	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))	maxCos	inf
3.0ms	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))	ux	-inf
3.0ms	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))	ux	inf

rewrite44.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary32`
835×	`expm1-log1p-u_binary32`
500×	`prod-diff_binary32`
95×	`add-sqr-sqrt_binary32`
90×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	205	25
2	2317	25

Stop Event

1×	node limit

Counts

3 → 67

simplify29.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

394×	`fma-def_binary32`
380×	`cancel-sign-sub-inv_binary32`
363×	`distribute-rgt-neg-in_binary32`
306×	`distribute-lft-neg-in_binary32`
265×	`sub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	227
1	100	203
2	252	195
3	852	185
4	3161	185

Stop Event

1×	node limit

Counts

93 → 85

prune70.0ms (3.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	129	2	131

Error

Counts

131 → 2

Alt Table

Status	Error	Program
✓	0.6b	(fma.f32 (pow.f32 (cbrt.f32 (-.f32 1 ux)) 2) (cbrt.f32 (-.f32 1 ux)) (*.f32 ux maxCos))
✓	0.0b	(fma.f32 ux (+.f32 maxCos -1) 1)

Compiler

Compiled 2158 to 1454 computations (32.6% saved)

regimes97.0ms (4.6%)

Accuracy

Total 0.0b remaining (39.1%)

Threshold costs 0.0b (39.1%)

Counts

25 → 1

Compiler

Compiled 1302 to 993 computations (23.7% 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

end37.0ms (1.7%)

Stop Event

1×

done

Compiler

Compiled 44 to 34 computations (22.7% 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	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

Details

analyze4.0ms (0.2%)

sample1.5s (69.3%)

preprocess41.0ms (1.9%)

simplify15.0ms (0.7%)

prune3.0ms (0.1%)

localize14.0ms (0.7%)

series7.0ms (0.3%)

rewrite43.0ms (2%)

simplify22.0ms (1.1%)

prune41.0ms (2%)

localize12.0ms (0.6%)

series5.0ms (0.2%)

rewrite32.0ms (1.5%)

simplify19.0ms (0.9%)

prune20.0ms (0.9%)

localize26.0ms (1.2%)

series67.0ms (3.2%)

rewrite44.0ms (2.1%)

simplify29.0ms (1.4%)

prune70.0ms (3.3%)

regimes97.0ms (4.6%)

simplify2.0ms (0.1%)

end37.0ms (1.7%)

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