Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample1.6s

Algorithm

intervals

Results

1.5s	126×	body	5120	exit
77.0ms	256×	body	80	valid
7.0ms	384×	pre	80	true
1.0ms	2×	body	80	invalid

simplify100.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4777	115
1	4777	115

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 1.8b

Counts

2 → 2

localize61.0ms

Local error

Found 4 expressions with local error:

8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-log-exp_binary64`
20×	`add-sqr-sqrt_binary64`
12×	`diff-log_binary64` `distribute-lft-out--_binary64`
8×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate--l-_binary64` `add-cube-cbrt_binary64` `difference-of-sqr-1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 80

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)

series1.0s

Counts

4 → 12

Calls

4 calls:

261.0ms	(-.f64 (-.f64 1 z) 1)
261.0ms	(-.f64 (-.f64 1 z) 1)
260.0ms	(-.f64 (-.f64 1 z) 1)
268.0ms	(-.f64 (-.f64 1 z) 1)

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36

simplify104.0ms

Counts

92 → 92

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5235	788

prune653.0ms

Filtered

72 candidates to 92 candidates (-27.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 1.8b

Counts

94 → 3

localize65.0ms

Local error

Found 4 expressions with local error:

8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)
59.9b	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
19×	`add-log-exp_binary64`
16×	`add-sqr-sqrt_binary64`
9×	`diff-log_binary64` `distribute-lft-out--_binary64`
6×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`flip3--_binary64` `associate--l-_binary64` `difference-of-sqr-1_binary64` `flip--_binary64` `associate--l+_binary64`
1×	`remove-posit16`

Counts

4 → 69

Calls

4 calls:

15.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
1.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(-.f64 (-.f64 1 z) 1)
258.0ms	(-.f64 (-.f64 1 z) 1)
263.0ms	(-.f64 (-.f64 1 z) 1)
153.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	38	1950
1	38	1950
0	16	9
1	16	9
0	38	1950
1	38	1950
0	16	9
1	16	9
0	1	3
1	1	3
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36

simplify101.0ms

Counts

81 → 81

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4842	642
1	4842	642

prune527.0ms

Filtered

63 candidates to 81 candidates (-28.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Merged error: 1.8b

Counts

84 → 2

localize68.0ms

Local error

Found 4 expressions with local error:

8.0b	(-.f64 (-.f64 1 z) 1)
8.0b	(-.f64 (-.f64 1 z) 1)
59.9b	(posit16->binary64 (binary64->posit16 (neg.f64 z)))
59.9b	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
14×	`add-log-exp_binary64`
12×	`add-sqr-sqrt_binary64`
6×	`diff-log_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
2×	`flip3--_binary64` `associate--l-_binary64` `difference-of-sqr-1_binary64` `remove-posit16` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 58

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
1.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))
1.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(-.f64 (-.f64 1 z) 1)
261.0ms	(-.f64 (-.f64 1 z) 1)
157.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))
157.0ms	(posit16->binary64 (binary64->posit16 (neg.f64 z)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	38	1950
1	38	1950
0	16	9
1	16	9
0	38	1950
1	38	1950
0	16	9
1	16	9
0	1	3
1	1	3
0	38	1950
1	38	1950
0	16	9
1	16	9
0	38	1950
1	38	1950
0	16	9
1	16	9
0	1	3
1	1	3
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36
0	179	75
1	179	75
0	6	9
1	6	9
0	179	75
1	179	75
0	6	9
1	6	9
0	4947	36
1	4947	36

simplify101.0ms

Counts

70 → 70

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4842	496
1	4842	496

prune377.0ms

Filtered

54 candidates to 70 candidates (-29.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	70	2	72

Merged error: 1.8b

Counts

72 → 2

localize58.0ms

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
44×	`add-log-exp_binary64` `frac-add_binary64`
31×	`distribute-lft-out_binary64` `sum-log_binary64`
10×	`add-exp-log_binary64`
9×	`flip3-+_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
7×	`prod-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `+-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `associate-r/_binary64` `associate-l_binary64` `pow-sub_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `pow-exp_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

101.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
19.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))
25.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

series1.6s

Counts

4 → 10

Calls

4 calls:

733.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
430.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))
484.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	504	868
1	504	868
0	82	284
1	82	284
0	504	868
1	504	868
0	82	284
1	82	284
0	4950	45
1	4950	45
0	754	2163
1	754	2163
0	5310	2141
0	754	2163
1	754	2163
0	5310	2141
0	1	3
1	1	3
0	1429	1568
1	1429	1568
0	4867	1347
1	4867	1347
0	1429	1568
1	1429	1568
0	4867	1347
1	4867	1347
0	1047	207
1	1047	207

simplify109.0ms

Counts

100 → 100

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4970	8055
1	4970	8055

prune599.0ms

Filtered

73 candidates to 100 candidates (-37.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	95	7	102

Merged error: 0.2b

Counts

102 → 7

regimes124.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	206	589
1	206	589

end0.0ms

sample51.0s

Algorithm

intervals

Results

47.9s	3973×	body	5120	exit
2.5s	8000×	body	80	valid
213.0ms	12045×	pre	80	true
24.0ms	72×	body	80	invalid

Details

analyze1.7s

sample1.6s

simplify100.0ms

prune15.0ms

localize61.0ms

rewrite41.0ms

series1.0s

simplify104.0ms

prune653.0ms

localize65.0ms

rewrite37.0ms

series932.0ms

simplify101.0ms

prune527.0ms

localize68.0ms

rewrite22.0ms

series840.0ms

simplify101.0ms

prune377.0ms

localize58.0ms

rewrite152.0ms

series1.6s

simplify109.0ms

prune599.0ms

regimes124.0ms

bsearch0.0ms

simplify14.0ms

end0.0ms

sample51.0s

Profiling