Details

analyze10.0ms (0.1%)

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 (12.1%)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify17.0ms (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)

localize14.0ms (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 (0.5%)

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 (0.2%)

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
	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.0s (81.6%)

Counts

2 → 48

Calls

2 calls:

10.0s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
17.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`exp-prod_binary32`
3×	`*-un-lft-identity_binary32`
3×	`add-sqr-sqrt_binary32`
3×	`add-cube-cbrt_binary32`
3×	`add-log-exp_binary32`

Counts

2 → 25

Calls

2 calls:

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

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

482×	`times-frac_binary32`
299×	`sub-neg_binary32`
216×	`distribute-neg-in_binary32`
200×	`distribute-rgt-in_binary32`
200×	`cancel-sign-sub-inv_binary32`

Counts

73 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	2004
1	654	1755
2	2386	1691
3	5067	1691

prune79.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

111 → 3

Alt Table

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

Compiler

Compiled 2357 to 1318 computations (44.1% saved)

localize24.0ms (0.2%)

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))))

series64.0ms (0.5%)

Counts

2 → 32

Calls

2 calls:

60.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))
4.0ms	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (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:

5.0ms	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
3.0ms	(sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux)))

simplify96.0ms (0.8%)

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

prune167.0ms (1.4%)

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
✓	0.4b	(*.f32 (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))) (sqrt.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(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)

regimes79.0ms (0.6%)

Accuracy

Total 0.0b remaining (83.6%)

Threshold costs 0.0b (83.6%)

Counts

18 → 1

Compiler

Compiled 846 to 625 computations (26.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`*-commutative_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	14	8
3	16	8
4	17	8
5	16	8

end47.0ms (0.4%)

Compiler: Compiled 55 to 37 computations (32.7% saved)

Details

analyze10.0ms (0.1%)

sample1.5s (12.1%)

simplify17.0ms (0.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify59.0ms (0.5%)

prune19.0ms (0.2%)

localize19.0ms (0.2%)

series10.0s (81.6%)

rewrite2.0ms (0%)

simplify62.0ms (0.5%)

prune79.0ms (0.6%)

localize24.0ms (0.2%)

series64.0ms (0.5%)

rewrite13.0ms (0.1%)

simplify96.0ms (0.8%)

prune167.0ms (1.4%)

regimes79.0ms (0.6%)

simplify2.0ms (0%)

end47.0ms (0.4%)

Profiling