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)

sample805.0ms (53.1%)

Symmetry

(sort a b)

Results

767.0ms

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))

rewrite9.0ms (0.6%)

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:

6.0ms

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

simplify66.0ms (4.3%)

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

prune33.0ms (2.2%)

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
	0.2b	(*.f64 b (fma.f64 2 a b))
✓	0.0b	(*.f64 (+.f64 a b) (+.f64 a b))
▶	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

Compiler

Compiled 938 to 292 computations (68.9% saved)

localize7.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

series10.0ms (0.7%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(+.f64 (*.f64 2 (*.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

rewrite9.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
3×	`sum-log_binary64`
1×	`+-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`flip-+_binary64`

Counts

1 → 16

Calls

1 calls:

9.0ms

(+.f64 (*.f64 2 (*.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))

simplify63.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

559×	`fma-neg_binary64`
415×	`distribute-rgt-out_binary64`
388×	`associate-l_binary64`
320×	`associate-r_binary64`
288×	`fma-def_binary64`

Counts

28 → 34

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	494
1	138	416
2	540	363
3	2532	363
4	4928	363
5	4992	363

prune25.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	35	2	37

Error

Counts

37 → 2

Alt Table

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

Compiler

Compiled 657 to 387 computations (41.1% saved)

localize10.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
✓	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
✓	3.3b	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))

series25.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))
8.0ms	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
6.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 32

Calls

3 calls:

0.0ms	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))
0.0ms	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
0.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))

simplify106.0ms (7%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
581×	`associate-l_binary64`
478×	`associate-r_binary64`
432×	`fma-neg_binary64`
348×	`associate-+l+_binary64`

Counts

104 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1743
1	248	1485
2	840	1419
3	3872	1412
4	4976	1412
5	4999	1412
6	4966	1412

prune51.0ms (3.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	75	2	77

Error

Counts

77 → 2

Alt Table

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

Compiler

Compiled 1400 to 777 computations (44.5% saved)

regimes70.0ms (4.6%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Counts

17 → 1

Compiler

Compiled 734 to 481 computations (34.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	9	16

end204.0ms (13.5%)

Compiler: Compiled 80 to 51 computations (36.3% saved)

Details

analyze1.0ms (0.1%)

sample805.0ms (53.1%)

simplify8.0ms (0.6%)

prune1.0ms (0.1%)

localize3.0ms (0.2%)

series6.0ms (0.4%)

rewrite9.0ms (0.6%)

simplify66.0ms (4.3%)

prune33.0ms (2.2%)

localize7.0ms (0.5%)

series10.0ms (0.7%)

rewrite9.0ms (0.6%)

simplify63.0ms (4.2%)

prune25.0ms (1.6%)

localize10.0ms (0.6%)

series25.0ms (1.6%)

rewrite2.0ms (0.1%)

simplify106.0ms (7%)

prune51.0ms (3.3%)

regimes70.0ms (4.6%)

simplify2.0ms (0.1%)

end204.0ms (13.5%)

Profiling