Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample866.0ms (64.2%)

Symmetry

(sort a b)

Results

831.0ms

8256×

body

128

valid

Compiler

Compiled 57 to 34 computations (40.4% saved)

simplify8.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

70×	`fma-def_binary64`
24×	`associate-+l+_binary64`
18×	`associate-+r+_binary64`
10×	`distribute-rgt-in_binary64`
8×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	12	10
2	26	10
3	46	10
4	81	10
5	101	10
6	117	10
7	130	10
8	132	10
9	132	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))

Compiler

Compiled 27 to 12 computations (55.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))

series6.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (+.f64 a b) (+.f64 a b))

rewrite14.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`distribute-lft-out_binary64`
6×	`swap-sqr_binary64`

Counts

1 → 42

Calls

1 calls:

12.0ms

(*.f64 (+.f64 a b) (+.f64 a b))

simplify53.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-+l+_binary64`
594×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
327×	`fma-def_binary64`

Counts

66 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	994
1	200	853
2	739	757
3	2462	692
4	5240	692

prune31.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
	0.9b	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))
▶	0.1b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 930 to 282 computations (69.7% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 b (fma.f64 2 a b))

series6.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 b (fma.f64 2 a b))

rewrite4.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

3.0ms

(*.f64 b (fma.f64 2 a b))

simplify87.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
610×	`distribute-lft-in_binary64`
425×	`fma-def_binary64`
354×	`*-commutative_binary64`
330×	`associate-/l/_binary64`

Counts

46 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	507
1	82	413
2	238	413
3	617	413
4	2304	413
5	2439	413
6	3040	413
7	4552	413
8	4968	413

prune15.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
▶	0.9b	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))
✓	0.1b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 377 to 205 computations (45.6% saved)

localize6.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
✓	0.1b	(log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b)))
✓	0.9b	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))

series27.0ms (2%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b)))
6.0ms	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b)))
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))

simplify47.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

937×	`times-frac_binary64`
614×	`associate-/l*_binary64`
438×	`fma-def_binary64`
209×	`cancel-sign-sub-inv_binary64`
174×	`sub-neg_binary64`

Counts

70 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1537
1	441	1374
2	1575	1265
3	5254	1265

prune73.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Error

Counts

161 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
✓	0.9b	(expm1.f64 (log1p.f64 (*.f64 (+.f64 a b) (+.f64 a b))))
✓	0.1b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 2854 to 1310 computations (54.1% saved)

regimes48.0ms (3.6%)

Accuracy

Total 0.0b remaining (19.6%)

Threshold costs 0.0b (19.6%)

Counts

12 → 1

Compiler

Compiled 428 to 290 computations (32.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	6	10
2	6	10

end47.0ms (3.5%)

Remove: (sort a b)
Compiler: Compiled 64 to 31 computations (51.6% saved)

Details

analyze1.0ms (0.1%)

sample866.0ms (64.2%)

simplify8.0ms (0.6%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.4%)

rewrite14.0ms (1%)

simplify53.0ms (3.9%)

prune31.0ms (2.3%)

localize4.0ms (0.3%)

series6.0ms (0.4%)

rewrite4.0ms (0.3%)

simplify87.0ms (6.5%)

prune15.0ms (1.1%)

localize6.0ms (0.5%)

series27.0ms (2%)

rewrite1.0ms (0.1%)

simplify47.0ms (3.5%)

prune73.0ms (5.4%)

regimes48.0ms (3.6%)

simplify2.0ms (0.1%)

end47.0ms (3.5%)

Profiling