Details

analyze8.0ms (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)

sample182.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
18.0ms	256×	pre	128	true

Compiler

Compiled 46 to 34 computations (26.1% saved)

simplify38.0ms (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

prune6.0ms (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)

localize35.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite2.0ms (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:

1.0ms

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

simplify95.0ms (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

prune50.0ms (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)

localize51.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series21.0s (58.5%)

Counts

4 → 63

Calls

4 calls:

20.9s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
37.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
11.0ms	(-.f32 (*.f32 maxCos ux) ux)
8.0ms	(*.f32 maxCos ux)

rewrite24.0ms (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:

8.0ms	(*.f32 maxCos ux)
6.0ms	(-.f32 (*.f32 maxCos ux) ux)
2.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

simplify115.0ms (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 → 172

Iterations

Useful iterations: 2 (0.0ms)

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

prune197.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	172	2	174

Error

Counts

174 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
▶	0.1b	(exp.f32 (log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))))

Compiler

Compiled 3104 to 1595 computations (48.6% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux))))
✓	0.0b	(exp.f32 (log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))))
✓	0.0b	(expm1.f32 (-.f32 (*.f32 maxCos ux) ux))
✓	0.1b	(log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))

series11.1s (31.1%)

Counts

4 → 96

Calls

4 calls:

11.1s	(exp.f32 (log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))))
36.0ms	(log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux))))
19.0ms	(expm1.f32 (-.f32 (*.f32 maxCos ux) ux))
9.0ms	(log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

2.0ms	(exp.f32 (log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))))
1.0ms	(expm1.f32 (-.f32 (*.f32 maxCos ux) ux))
1.0ms	(log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))
1.0ms	(log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux))))

simplify193.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

482×	`times-frac_binary32`
409×	`fma-neg_binary32`
373×	`sub-neg_binary32`
283×	`fma-def_binary32`
247×	`associate-+r+_binary32`

Counts

143 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	2948
1	885	2649
2	3310	2565
3	4922	2565
4	5074	2565

prune201.0ms (0.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	164	2	166

Error

Counts

166 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f32 ux maxCos (-.f32 1 ux))
✓	0.1b	(exp.f32 (log1p.f32 (log1p.f32 (expm1.f32 (-.f32 (*.f32 maxCos ux) ux)))))

Compiler

Compiled 3498 to 1800 computations (48.5% saved)

regimes212.0ms (0.6%)

Accuracy

Total 0.0b remaining (79.4%)

Threshold costs 0.0b (79.4%)

Counts

23 → 1

Compiler

Compiled 990 to 721 computations (27.2% saved)

simplify4.0ms (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

end1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample2.2s (6.2%)

Algorithm

1×

intervals

Results

633.0ms	7998×	body	128	valid
516.0ms	8000×	pre	128	true
0.0ms	2×	body	256	valid

Compiler

Compiled 66 to 48 computations (27.3% saved)

Details

analyze8.0ms (0%)

sample182.0ms (0.5%)

simplify38.0ms (0.1%)

prune6.0ms (0%)

localize35.0ms (0.1%)

series10.0ms (0%)

rewrite2.0ms (0%)

simplify95.0ms (0.3%)

prune50.0ms (0.1%)

localize51.0ms (0.1%)

series21.0s (58.5%)

rewrite24.0ms (0.1%)

simplify115.0ms (0.3%)

prune197.0ms (0.6%)

localize57.0ms (0.2%)

series11.1s (31.1%)

rewrite7.0ms (0%)

simplify193.0ms (0.5%)

prune201.0ms (0.6%)

regimes212.0ms (0.6%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.2s (6.2%)

Profiling