Details

analyze6.0ms (0%)

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)

sample112.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	255×	body	128	valid
8.0ms	256×	pre	128	true
0.0ms	1×	body	256	valid

Compiler

Compiled 46 to 34 computations (26.1% 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)

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 (0.5%)

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

prune87.0ms (0.7%)

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	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 268 to 160 computations (40.3% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))

series10.1s (78.7%)

Counts

3 → 63

Calls

3 calls:

10.1s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
17.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
5.0ms	(-.f32 (*.f32 maxCos ux) ux)

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary32`
6×	`add-sqr-sqrt_binary32`
6×	`add-cube-cbrt_binary32`
6×	`add-log-exp_binary32`
4×	`expm1-log1p-u_binary32`

Counts

3 → 46

Calls

3 calls:

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

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-neg_binary32`
308×	`sub-neg_binary32`
267×	`cancel-sign-sub-inv_binary32`
226×	`unswap-sqr_binary32`
223×	`fma-def_binary32`

Counts

109 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2337
1	740	2054
2	3057	1971
3	4863	1971
4	5002	1971

prune136.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	144	2	146

Error

Counts

146 → 2

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (log1p.f32 (/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos))))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 2822 to 1465 computations (48.1% saved)

localize55.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos)))))
✓	0.1b	(pow.f32 (*.f32 ux maxCos) 3)
✓	0.2b	(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
✓	0.3b	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos))))

series159.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

81.0ms	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos))))
52.0ms	(log1p.f32 (/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos)))))
13.0ms	(pow.f32 (*.f32 ux maxCos) 3)
12.0ms	(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary32`
46×	`pow1_binary32`
39×	`times-frac_binary32`
32×	`difference-of-squares_binary32`
31×	`*-un-lft-identity_binary32`

Counts

4 → 143

Calls

4 calls:

15.0ms	(/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos))))
6.0ms	(.f32 (.f32 ux maxCos) (*.f32 ux maxCos))
2.0ms	(pow.f32 (*.f32 ux maxCos) 3)
0.0ms	(log1p.f32 (/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos)))))

simplify190.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

338×	`sub-neg_binary32`
262×	`fma-neg_binary32`
196×	`+-commutative_binary32`
191×	`associate-/l*_binary32`
187×	`associate-l_binary32`

Counts

239 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	7983
1	1040	7041
2	4122	6740
3	4959	6740
4	5016	6740

prune236.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	239	2	241

Error

Counts

241 → 2

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (/.f32 (-.f32 (pow.f32 (.f32 ux maxCos) 3) (pow.f32 ux 3)) (fma.f32 ux (fma.f32 ux maxCos ux) (.f32 (.f32 ux maxCos) (.f32 ux maxCos))))))
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))

Compiler

Compiled 9923 to 4719 computations (52.4% saved)

regimes339.0ms (2.6%)

Accuracy

Total 0.0b remaining (70.7%)

Threshold costs 0.0b (70.7%)

Counts

92 → 1

Compiler

Compiled 6294 to 4001 computations (36.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
2×	`*-commutative_binary32`
2×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`/-rgt-identity_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	20	13
3	22	13
4	23	13
5	22	13

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample1.2s (9%)

Algorithm

1×

intervals

Results

326.0ms	7997×	body	128	valid
278.0ms	8000×	pre	128	true
0.0ms	3×	body	256	valid

Compiler

Compiled 85 to 55 computations (35.3% saved)

Details

analyze6.0ms (0%)

sample112.0ms (0.9%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify61.0ms (0.5%)

prune87.0ms (0.7%)

localize19.0ms (0.1%)

series10.1s (78.7%)

rewrite6.0ms (0%)

simplify93.0ms (0.7%)

prune136.0ms (1.1%)

localize55.0ms (0.4%)

series159.0ms (1.2%)

rewrite40.0ms (0.3%)

simplify190.0ms (1.5%)

prune236.0ms (1.8%)

regimes339.0ms (2.6%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (9%)

Profiling