Details

analyze3.3s (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.1%	99.9%	0
0%	0.1%	99.9%	1
0%	0.1%	99.9%	2
0%	0.1%	99.9%	3
0%	0.1%	99.9%	4
0%	0.1%	99.9%	5
0%	0.1%	99.9%	6
0%	0.1%	99.9%	7
0%	0.1%	99.9%	8
0%	0.1%	99.9%	9
0%	0.1%	99.9%	10
0%	0.1%	99.9%	11
0%	0.1%	99.9%	12
0%	0.1%	99.9%	13
0%	0.1%	99.9%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample1.6s (6.4%)

Results

1.6s	8254×	body	128	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 43 to 31 computations (27.9% saved)

simplify18.0ms (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)

localize15.0ms (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))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary32`
1×	`add-sqr-sqrt_binary32`
1×	`add-cube-cbrt_binary32`
1×	`add-cbrt-cube_binary32`
1×	`add-exp-log_binary32`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-neg_binary32`
470×	`times-frac_binary32`
313×	`distribute-rgt-in_binary32`
309×	`neg-sub0_binary32`
301×	`distribute-lft-in_binary32`

Counts

34 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	331
1	45	278
2	99	277
3	292	277
4	1097	277
5	2072	277
6	4492	277
7	5251	277

prune15.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	2	27

Error

0.0b

Counts

27 → 2

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 268 to 160 computations (40.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 maxCos ux)
✓	0.0b	(-.f32 (*.f32 maxCos ux) ux)
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.2s (39.5%)

Counts

4 → 63

Calls

4 calls:

10.1s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
18.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
4.0ms	(-.f32 (*.f32 maxCos ux) ux)
4.0ms	(*.f32 maxCos ux)

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary32`
10×	`*-un-lft-identity_binary32`
9×	`add-cube-cbrt_binary32`
7×	`add-log-exp_binary32`
6×	`add-cbrt-cube_binary32`

Counts

4 → 66

Calls

4 calls:

3.0ms	(-.f32 (*.f32 maxCos ux) ux)
3.0ms	(*.f32 maxCos ux)
2.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

370×	`fma-neg_binary32`
309×	`sub-neg_binary32`
275×	`cancel-sign-sub-inv_binary32`
225×	`fma-def_binary32`
216×	`unswap-sqr_binary32`

Counts

129 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	2491
1	768	2188
2	3179	2084
3	4920	2084

prune180.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
▶	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 3127 to 1605 computations (48.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f32 maxCos ux)
	0.0b	(-.f32 (*.f32 maxCos ux) ux)
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.0b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series9.9s (38.4%)

Counts

1 → 24

Calls

1 calls:

9.9s	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`pow-unpow_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-sqr-sqrt_binary32`
3×	`unpow-prod-down_binary32`
3×	`add-cube-cbrt_binary32`

Counts

1 → 20

Calls

1 calls:

2.0ms

(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-neg_binary32`
642×	`fma-def_binary32`
512×	`div-sub_binary32`
422×	`log-prod_binary32`
335×	`log-div_binary32`

Counts

44 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	592
1	169	515
2	355	509
3	940	509
4	2625	509
5	4705	509
6	4925	509
7	4962	509
8	4772	509

prune102.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 3362 to 1594 computations (52.6% saved)

regimes83.0ms (0.3%)

Accuracy

Total 0.0b remaining (89.1%)

Threshold costs 0.0b (89.1%)

Counts

21 → 1

Compiler

Compiled 1238 to 873 computations (29.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end37.0ms (0.1%)

Compiler: Compiled 50 to 35 computations (30% saved)

Details

analyze3.3s (12.8%)

sample1.6s (6.4%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify59.0ms (0.2%)

prune15.0ms (0.1%)

localize19.0ms (0.1%)

series10.2s (39.5%)

rewrite11.0ms (0%)

simplify76.0ms (0.3%)

prune180.0ms (0.7%)

localize23.0ms (0.1%)

series9.9s (38.4%)

rewrite2.0ms (0%)

simplify102.0ms (0.4%)

prune102.0ms (0.4%)

regimes83.0ms (0.3%)

simplify2.0ms (0%)

end37.0ms (0.1%)

Profiling