Details

analyze2.3s (35%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample47.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	252×	body	80	valid
1.0ms	3×	body	320	invalid
1.0ms	2×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	6×	body	80	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	320	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5054	43

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.6b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
30.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `times-frac_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 59

Calls

4 calls:

18.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
11.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series579.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
143.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
111.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
91.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify148.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4983	1327
1	4983	1327

prune114.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.8b

Counts

72 → 3

Compiler

Compiled 2460 to 1230 computations (50% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64`
2×	`add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

2 → 35

Calls

2 calls:

18.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
15.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series341.0ms (5.2%)

Counts

2 → 6

Calls

2 calls:

232.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
108.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5484	740

prune54.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0.8b

Counts

44 → 4

Compiler

Compiled 1073 to 615 computations (42.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
30.2b	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
30.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `remove-posit16` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 55

Calls

4 calls:

13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
11.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
1.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

series385.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
106.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
95.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
44.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4974	1205
1	4974	1205

prune110.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	67	4	71

Merged error: 0.8b

Counts

71 → 4

Compiler

Compiled 2427 to 1274 computations (47.5% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))) l)

0.0b

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

24.7b

(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
5×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
4×	`pow1_binary64` `add-exp-log_binary64`
3×	`pow-unpow_binary64` `add-cbrt-cube_binary64` `insert-posit16`
2×	`difference-of-squares_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `remove-posit16` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 44

Calls

3 calls:

16.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

4.0ms

(+.f64 (posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))) l)

1.0ms

(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))

series228.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

109.0ms

(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

84.0ms

(+.f64 (posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2))) l)

35.0ms

(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5051	920

prune63.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	53	4	57

Merged error: 0.8b

Counts

57 → 4

Compiler

Compiled 1330 to 768 computations (42.3% saved)

regimes75.0ms (1.1%)

Compiler: Compiled 520 to 490 computations (5.8% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms (0%)

sample1.6s (23.7%)

Algorithm

1×

intervals

Results

852.0ms	7846×	body	80	valid
42.0ms	65×	body	1280	invalid
38.0ms	48×	body	1280	valid
38.0ms	89×	body	640	invalid
28.0ms	63×	body	640	valid
27.0ms	261×	body	80	invalid
20.0ms	64×	body	320	invalid
9.0ms	28×	body	160	invalid
8.0ms	27×	body	320	valid
5.0ms	5×	body	2560	invalid
3.0ms	16×	body	160	valid

Compiler

Compiled 149 to 133 computations (10.7% saved)

Details

analyze2.3s (35%)

sample47.0ms (0.7%)

simplify83.0ms (1.3%)

prune5.0ms (0.1%)

localize27.0ms (0.4%)

rewrite55.0ms (0.8%)

series579.0ms (8.8%)

simplify148.0ms (2.2%)

prune114.0ms (1.7%)

localize14.0ms (0.2%)

rewrite35.0ms (0.5%)

series341.0ms (5.2%)

simplify57.0ms (0.9%)

prune54.0ms (0.8%)

localize23.0ms (0.3%)

rewrite38.0ms (0.6%)

series385.0ms (5.8%)

simplify104.0ms (1.6%)

prune110.0ms (1.7%)

localize15.0ms (0.2%)

rewrite22.0ms (0.3%)

series228.0ms (3.5%)

simplify96.0ms (1.5%)

prune63.0ms (1%)

regimes75.0ms (1.1%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.6s (23.7%)

Profiling