Details

sample392.0ms

Algorithm

intervals

Results

101.0ms	95×	body	1280	valid
60.0ms	42×	body	10240	exit
45.0ms	30×	body	320	valid
42.0ms	50×	body	640	valid
31.0ms	21×	body	1280	nan
27.0ms	168×	body	80	valid
21.0ms	184×	body	80	nan
18.0ms	23×	body	640	nan
9.0ms	16×	body	320	nan
7.0ms	22×	body	160	valid
3.0ms	9×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
6	2681
5	735
4	218
3	82
2	34
1	17
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1 n))
1.2b	(pow (+ x 1) (/ 1 n))
2.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 82

Calls

3 calls:

5.0ms	(pow x (/ 1 n))
21.0ms	(pow (+ x 1) (/ 1 n))
99.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series440.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(pow x (/ 1 n))
120.0ms	(pow (+ x 1) (/ 1 n))
245.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.6s

Counts

91 → 91

Iterations

Iter	Nodes
3	3490
2	1217
1	467
0	176

prune861.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 18.8b

localize18.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1 n))
1.2b	(pow (+ x 1) (/ 1 n))
2.7b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 82

Calls

3 calls:

3.0ms	(pow x (/ 1 n))
9.0ms	(pow (+ x 1) (/ 1 n))
70.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

series505.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(pow x (/ 1 n))
143.0ms	(pow (+ x 1) (/ 1 n))
291.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

simplify2.6s

Counts

91 → 91

Iterations

Iter	Nodes
3	3490
2	1217
1	467
0	176

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 18.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ -1/2 (* (* n x) x))
1.1b	(/ (log x) (* n n))
2.0b	(+ (/ (/ 1 x) n) (/ -1/2 (* (* n x) x)))
6.2b	(/ (/ (log x) (* n n)) x)

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
27×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
25×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-/l*`
10×	`pow1` `cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`log-pow` `add-log-exp`
5×	`associate-/r*` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `frac-add` `flip-+` `distribute-lft-out` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

29.0ms	(/ -1/2 (* (* n x) x))
17.0ms	(/ (log x) (* n n))
49.0ms	(+ (/ (/ 1 x) n) (/ -1/2 (* (* n x) x)))
36.0ms	(/ (/ (log x) (* n n)) x)

series302.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ -1/2 (* (* n x) x))
97.0ms	(/ (log x) (* n n))
72.0ms	(+ (/ (/ 1 x) n) (/ -1/2 (* (* n x) x)))
98.0ms	(/ (/ (log x) (* n n)) x)

simplify765.0ms

Counts

127 → 127

Iterations

Iter	Nodes
2	2291
1	579
0	217

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.7b

localize54.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (log x) (* n n))
2.0b	(+ (/ (/ 1 x) n) (log (exp (/ -1/2 (* (* n x) x)))))
2.0b	(log (exp (/ -1/2 (* (* n x) x))))
6.2b	(/ (/ (log x) (* n n)) x)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
30×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
15×	`log-pow`
12×	`pow1` `associate-/l*`
7×	`cbrt-undiv` `exp-prod` `div-exp` `div-inv`
6×	`log-prod`
5×	`add-log-exp`
4×	`associate-/r*` `insert-posit16`
3×	`associate-+r+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `rem-log-exp` `flip-+` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

8.0ms	(/ (log x) (* n n))
65.0ms	(+ (/ (/ 1 x) n) (log (exp (/ -1/2 (* (* n x) x)))))
30.0ms	(log (exp (/ -1/2 (* (* n x) x))))
14.0ms	(/ (/ (log x) (* n n)) x)

series267.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (log x) (* n n))
62.0ms	(+ (/ (/ 1 x) n) (log (exp (/ -1/2 (* (* n x) x)))))
28.0ms	(log (exp (/ -1/2 (* (* n x) x))))
90.0ms	(/ (/ (log x) (* n n)) x)

simplify4.7s

Counts

126 → 126

Iterations

Iter	Nodes
3	7560
2	1604
1	488
0	211

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.7b

regimes462.0ms

Accuracy

86.3% (1.2b remaining)

Error of 22.1b against oracle of 20.9b and baseline of 29.7b

bsearch350.0ms

Steps

Iters	Range		Point
11	0.0010844106832778484	5.056791261029699e+17	1591665190.7901402
8	-13794.795225653274	-35.89559594794403	-13657.800064202142

simplify8.0ms

Iterations

Iter	Nodes
2	44
1	44
0	36

end0.0ms

sample11.2s

Algorithm

intervals

Results

3.5s	3152×	body	1280	valid
1.6s	4775×	body	80	valid
1.4s	1198×	body	10240	exit
1.3s	1591×	body	640	valid
796.0ms	639×	body	1280	nan
647.0ms	5145×	body	80	nan
532.0ms	624×	body	640	nan
448.0ms	874×	body	320	valid
248.0ms	418×	body	320	nan
138.0ms	428×	body	160	valid
80.0ms	175×	body	160	nan