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 (6.8%)

Results

1.5s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

simplify19.0ms (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)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(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))

simplify62.0ms (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)

localize18.0ms (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)))
✓	0.1b	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))

series10.4s (46.3%)

Counts

3 → 63

Calls

3 calls:

10.4s	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))
17.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
4.0ms	(-.f32 (*.f32 maxCos ux) ux)

rewrite8.0ms (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)
2.0ms	(log1p.f32 (-.f32 (*.f32 maxCos ux) ux))
1.0ms	(exp.f32 (log1p.f32 (-.f32 (*.f32 maxCos ux) ux)))

simplify135.0ms (0.6%)

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

prune96.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	145	2	147

Error

Counts

147 → 2

Alt Table

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

Compiler

Compiled 2788 to 1451 computations (48% saved)

localize25.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series9.9s (43.7%)

Counts

1 → 24

Calls

1 calls:

9.9s	(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

prune79.0ms (0.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	149	2	151

Error

Counts

151 → 2

Alt Table

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

Compiler

Compiled 2992 to 1436 computations (52% saved)

regimes87.0ms (0.4%)

Accuracy

Total 0.0b remaining (86.3%)

Threshold costs 0.0b (86.3%)

Counts

22 → 1

Compiler

Compiled 906 to 677 computations (25.3% saved)

simplify3.0ms (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

end37.0ms (0.2%)

Compiler: Compiled 40 to 28 computations (30% saved)

Details

analyze5.0ms (0%)

sample1.5s (6.8%)

simplify19.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series5.0ms (0%)

rewrite1.0ms (0%)

simplify62.0ms (0.3%)

prune19.0ms (0.1%)

localize18.0ms (0.1%)

series10.4s (46.3%)

rewrite8.0ms (0%)

simplify135.0ms (0.6%)

prune96.0ms (0.4%)

localize25.0ms (0.1%)

series9.9s (43.7%)

rewrite2.0ms (0%)

simplify102.0ms (0.5%)

prune79.0ms (0.3%)

regimes87.0ms (0.4%)

simplify3.0ms (0%)

end37.0ms (0.2%)

Profiling