Details

analyze2.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample42.0ms (6.3%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

7.0ms	256×	pre	128	true
5.0ms	256×	body	128	valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify9.0ms (1.3%)

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 (0.2%)

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 (0.5%)

Local error

Found 1 expressions with local error:

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

series7.0ms (1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite8.0ms (1.3%)

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))

simplify48.0ms (7.3%)

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

prune36.0ms (5.5%)

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

0.0b

Counts

65 → 3

Alt Table

Status	Error	Program
✓	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)))
	0.2b	(*.f64 b (fma.f64 2 a b))

Compiler

Compiled 938 to 292 computations (68.9% saved)

localize8.0ms (1.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (3%)

Counts

3 → 18

Calls

3 calls:

7.0ms	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))
6.0ms	(+.f64 (pow.f64 a 2) (pow.f64 b 2))
6.0ms	(.f64 2 (.f64 a b))

rewrite21.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`fma-def_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

3 → 59

Calls

3 calls:

8.0ms	(+.f64 (.f64 2 (.f64 a b)) (+.f64 (pow.f64 a 2) (pow.f64 b 2)))
5.0ms	(+.f64 (pow.f64 a 2) (pow.f64 b 2))
4.0ms	(.f64 2 (.f64 a b))

simplify58.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-neg_binary64`
654×	`associate-l_binary64`
513×	`associate-r_binary64`
471×	`fma-def_binary64`
319×	`distribute-rgt-neg-in_binary64`

Counts

77 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	905
1	248	787
2	837	728
3	3406	728
4	5028	728

prune78.0ms (11.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	95	3	98

Error

Counts

98 → 3

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
✓	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 1796 to 1090 computations (39.3% saved)

localize11.0ms (1.7%)

Local error

Found 3 expressions with local error:

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

series27.0ms (4.1%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(fma.f64 b (fma.f64 2 a b) (*.f64 a a))
10.0ms	(expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a)))
7.0ms	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))

rewrite2.0ms (0.4%)

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))))

simplify110.0ms (16.7%)

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

prune58.0ms (8.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (fma.f64 b (fma.f64 2 a b) (*.f64 a a))))
✓	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 1443 to 811 computations (43.8% saved)

regimes93.0ms (14.2%)

Counts: 25 → 1
Compiler: Compiled 1098 to 761 computations (30.7% saved)

simplify2.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	7	12

end6.0ms (0.9%)

Compiler: Compiled 33 to 18 computations (45.5% saved)

sample8.0ms (1.2%)

Algorithm

1×

intervals

Results

0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false
0.0ms	1×	pre	128	false

Compiler

Compiled 26 to 17 computations (34.6% saved)

Details

analyze2.0ms (0.3%)

sample42.0ms (6.3%)

simplify9.0ms (1.3%)

prune1.0ms (0.2%)

localize3.0ms (0.5%)

series7.0ms (1%)

rewrite8.0ms (1.3%)

simplify48.0ms (7.3%)

prune36.0ms (5.5%)

localize8.0ms (1.2%)

series20.0ms (3%)

rewrite21.0ms (3.2%)

simplify58.0ms (8.9%)

prune78.0ms (11.9%)

localize11.0ms (1.7%)

series27.0ms (4.1%)

rewrite2.0ms (0.4%)

simplify110.0ms (16.7%)

prune58.0ms (8.8%)

regimes93.0ms (14.2%)

simplify2.0ms (0.3%)

end6.0ms (0.9%)

sample8.0ms (1.2%)

end0.0ms (0%)

Profiling