Details

sample219.0ms

Algorithm

intervals

Results

87.0ms	110×	body	1280	valid
27.0ms	35×	body	10240	exit
26.0ms	55×	body	640	valid
13.0ms	141×	body	80	valid
13.0ms	19×	body	1280	nan
9.0ms	144×	body	80	nan
8.0ms	16×	body	640	nan
5.0ms	19×	body	320	valid
4.0ms	12×	body	320	nan
4.0ms	16×	body	160	valid
1.0ms	8×	body	160	nan

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	543
1	17	543
2	34	543
3	81	543
4	225	543
5	690	543
6	2902	543
done	5004	543

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize35.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.8b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite102.0ms

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` `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 → 79

Calls

3 calls:

6.0ms	(pow x (/ 1.0 n))
15.0ms	(pow (+ x 1.0) (/ 1.0 n))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series657.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms	(pow x (/ 1.0 n))
168.0ms	(pow (+ x 1.0) (/ 1.0 n))
391.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.7s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	189	47913
1	530	43582
2	1452	43260
3	4849	42631
done	5000	42631

prune526.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.8b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite311.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
27×	`unpow-prod-down`
26×	`pow-unpow`
22×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
14×	`sqr-pow`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
5×	`log-prod`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `pow-pow` `exp-sum` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
208.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
86.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow x (/ 1.0 n))
241.0ms	(pow (+ x 1.0) (/ 1.0 n))
433.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

121 → 121

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	234	72253
1	606	62746
2	1576	61942
done	5000	61194

prune781.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.8b

localize60.0ms

Local error

Found 4 expressions with local error:

2.3b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite666.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
40×	`unpow-prod-down`
38×	`*-un-lft-identity`
36×	`log-pow` `difference-of-squares`
32×	`sqrt-pow1`
30×	`exp-prod`
24×	`sqr-pow`
16×	`log-prod`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `add-cbrt-cube` `exp-sum` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 118

Calls

4 calls:

216.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
218.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
96.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
130.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series2.3s

Counts

4 → 12

Calls

4 calls:

746.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
757.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
372.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
418.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.1s

Counts

130 → 130

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	168	108908
1	351	99350
2	905	98302
3	2925	98146
done	5000	97986

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.8b

localize55.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (exp (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`unpow-prod-down`
27×	`difference-of-squares`
26×	`*-un-lft-identity`
18×	`sqr-pow`
11×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`pow1` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `log-pow` `flip--` `distribute-lft-out`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 86

Calls

4 calls:

5.0ms	(log (exp (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
84.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series3.2s

Counts

4 → 12

Calls

4 calls:

2.0s	(log (exp (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
427.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
320.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
398.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify4.4s

Counts

98 → 98

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	152	87053
1	363	81781
2	946	81295
3	3203	81138
done	5000	80794

prune837.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.8b

regimes445.0ms

Accuracy

80.5% (1.6b remaining)

Error of 22.2b against oracle of 20.6b and baseline of 29.0b

bsearch2.0ms

simplify18.0ms

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	52	2767
1	64	2767
done	64	2767

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.9s	3158×	body	1280	valid
999.0ms	1597×	body	640	valid
984.0ms	1207×	body	10240	exit
596.0ms	648×	body	1280	nan
573.0ms	4937×	body	80	valid
514.0ms	809×	body	320	valid
360.0ms	5012×	body	80	nan
342.0ms	633×	body	640	nan
106.0ms	326×	body	320	nan
97.0ms	420×	body	160	valid
33.0ms	179×	body	160	nan