Details

analyze5.0ms (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)

sample1.5s (6.9%)

Results

1.4s	8254×	body	128	valid
1.0ms	2×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% 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))

simplify59.0ms (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 (3 fresh and 0 done)

	Pruned	Kept	Total
New	23	3	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	3	27

Error

0.0b

Counts

27 → 3

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
	0.1b	(-.f32 (fma.f32 maxCos ux 1) ux)

Compiler

Compiled 299 to 182 computations (39.1% saved)

localize19.0ms (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)))
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series9.5s (43.9%)

Counts

4 → 63

Calls

4 calls:

9.5s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
17.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
4.0ms	(*.f32 maxCos ux)
4.0ms	(-.f32 (*.f32 maxCos ux) ux)

rewrite10.0ms (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:

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))

simplify69.0ms (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

prune108.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f32 1 (-.f32 (*.f32 maxCos ux) ux))
	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
▶	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 3135 to 1617 computations (48.4% saved)

localize24.0ms (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	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series9.8s (45.1%)

Counts

1 → 24

Calls

1 calls:

9.8s	(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 (0.5%)

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

prune101.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f32 1 (-.f32 (*.f32 maxCos ux) ux))
	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 3369 to 1606 computations (52.3% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f32 1 (-.f32 (*.f32 maxCos ux) ux))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`associate-+r+_binary32`
6×	`add-log-exp_binary32`
6×	`*-un-lft-identity_binary32`
4×	`add-sqr-sqrt_binary32`
4×	`add-cube-cbrt_binary32`

Counts

1 → 26

Calls

1 calls:

5.0ms

(+.f32 1 (-.f32 (*.f32 maxCos ux) ux))

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary32`
488×	`distribute-rgt-out_binary32`
347×	`associate-l_binary32`
345×	`exp-prod_binary32`
289×	`associate-r_binary32`

Counts

50 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	511
1	128	412
2	407	408
3	2028	408
4	4823	408
5	4972	408

prune60.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	114	3	117

Error

Counts

117 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f32 1 (-.f32 (*.f32 maxCos ux) ux))
	0.4b	(expm1.f32 (log1p.f32 (fma.f32 ux maxCos (-.f32 1 ux))))
✓	0.0b	(pow.f32 (E.f32) (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

Compiler

Compiled 1441 to 621 computations (56.9% saved)

regimes121.0ms (0.6%)

Accuracy

Total 0.0b remaining (87.9%)

Threshold costs 0.0b (87.9%)

Counts

35 → 1

Compiler

Compiled 1466 to 1073 computations (26.8% 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	8	13
1	13	13
2	19	13
3	21	13
4	22	13
5	21	13

end49.0ms (0.2%)

Compiler: Compiled 54 to 39 computations (27.8% saved)

Details

analyze5.0ms (0%)

sample1.5s (6.9%)

simplify18.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series4.0ms (0%)

rewrite1.0ms (0%)

simplify59.0ms (0.3%)

prune19.0ms (0.1%)

localize19.0ms (0.1%)

series9.5s (43.9%)

rewrite10.0ms (0%)

simplify69.0ms (0.3%)

prune108.0ms (0.5%)

localize24.0ms (0.1%)

series9.8s (45.1%)

rewrite2.0ms (0%)

simplify102.0ms (0.5%)

prune101.0ms (0.5%)

localize17.0ms (0.1%)

series4.0ms (0%)

rewrite6.0ms (0%)

simplify68.0ms (0.3%)

prune60.0ms (0.3%)

regimes121.0ms (0.6%)

simplify2.0ms (0%)

end49.0ms (0.2%)

Profiling