Details

analyze66.0ms (0.4%)

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)

sample36.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 46 to 34 computations (26.1% saved)

simplify38.0ms (0.2%)

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)

localize13.0ms (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))

simplify61.0ms (0.3%)

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

prune19.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Error

Counts

27 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 304 to 184 computations (39.5% 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)))
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series14.1s (81.4%)

Counts

4 → 63

Calls

4 calls:

14.1s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
19.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
5.0ms	(-.f32 (*.f32 maxCos ux) ux)
4.0ms	(*.f32 maxCos ux)

rewrite11.0ms (0.1%)

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:

4.0ms	(-.f32 (*.f32 maxCos ux) ux)
3.0ms	(*.f32 maxCos ux)
1.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

simplify78.0ms (0.5%)

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

prune122.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 3141 to 1613 computations (48.6% saved)

localize23.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
✓	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))

series140.0ms (0.8%)

Counts

2 → 32

Calls

2 calls:

74.0ms	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
65.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary32`
21×	`sqrt-prod_binary32`
18×	`pow1_binary32`
11×	`*-un-lft-identity_binary32`
11×	`add-cube-cbrt_binary32`

Counts

2 → 68

Calls

2 calls:

6.0ms	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
1.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-l_binary32`
524×	`fma-def_binary32`
489×	`associate-r_binary32`
419×	`sub-neg_binary32`
210×	`associate-+l+_binary32`

Counts

100 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1523
1	306	1329
2	992	1262
3	4365	1228
4	4958	1228
5	4945	1228

prune143.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	196	3	199

Error

Counts

199 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 4246 to 2762 computations (35% saved)

regimes175.0ms (1%)

Accuracy

Total 0.0b remaining (72%)

Threshold costs 0.0b (72%)

Counts

46 → 1

Compiler

Compiled 2158 to 1605 computations (25.6% saved)

simplify5.0ms (0%)

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

end1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample2.1s (12.4%)

Algorithm

1×

intervals

Results

601.0ms	8000×	body	128	valid
497.0ms	8000×	pre	128	true

Compiler

Compiled 83 to 59 computations (28.9% saved)

Details

analyze66.0ms (0.4%)

sample36.0ms (0.2%)

simplify38.0ms (0.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify61.0ms (0.3%)

prune19.0ms (0.1%)

localize19.0ms (0.1%)

series14.1s (81.4%)

rewrite11.0ms (0.1%)

simplify78.0ms (0.5%)

prune122.0ms (0.7%)

localize23.0ms (0.1%)

series140.0ms (0.8%)

rewrite13.0ms (0.1%)

simplify99.0ms (0.6%)

prune143.0ms (0.8%)

regimes175.0ms (1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.1s (12.4%)

Profiling