Details

sample218.0ms

Algorithm

intervals

Results

59.0ms	90×	body	1280	valid
42.0ms	67×	body	640	valid
23.0ms	39×	body	10240	exit
16.0ms	172×	body	80	valid
11.0ms	14×	body	1280	nan
10.0ms	21×	body	640	nan
10.0ms	169×	body	80	nan
10.0ms	31×	body	320	valid
4.0ms	11×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	5×	body	160	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	231	13
5	694	13
6	3452	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize24.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow (+ x 1.0) (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite186.0ms

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:

15.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow x (/ 1.0 n))
161.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series623.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(pow (+ x 1.0) (/ 1.0 n))
92.0ms	(pow x (/ 1.0 n))
349.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	190	1337
1	473	1246
2	1193	1206
3	3609	1183
done	5000	1183

prune412.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.8b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
0.8b	(pow x (/ 1.0 n))
3.0b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
28×	`cbrt-prod`
26×	`pow-unpow`
18×	`times-frac`
13×	`pow1`
12×	`cbrt-div`
10×	`unpow-prod-down`
9×	`swap-sqr`
8×	`add-exp-log`
7×	`pow1/3` `associate-r` `associate-l` `distribute-lft-out`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`pow-pow`
2×	`pow-to-exp` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv` `sqr-pow`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

79.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
23.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
9.0ms	(pow x (/ 1.0 n))
90.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series2.0s

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
472.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
111.0ms	(pow x (/ 1.0 n))
1.2s	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify1.6s

Counts

136 → 136

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	315	2362
1	806	2164
2	2276	1911
done	5000	1879

prune637.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.8b	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
0.8b	(pow (pow x 1.0) (/ 1 n))
3.0b	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow (pow x 1.0) (/ 1 n)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
28×	`cbrt-prod`
26×	`pow-unpow`
18×	`times-frac`
17×	`unpow-prod-down`
12×	`pow1` `cbrt-div`
9×	`add-exp-log` `swap-sqr`
7×	`pow1/3` `associate-r` `associate-l` `distribute-lft-out`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

55.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
24.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
16.0ms	(pow (pow x 1.0) (/ 1 n))
78.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow (pow x 1.0) (/ 1 n)))

series2.2s

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
469.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
164.0ms	(pow (pow x 1.0) (/ 1 n))
1.4s	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow (pow x 1.0) (/ 1 n)))

simplify1.8s

Counts

142 → 142

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	347	2555
1	878	2335
2	2380	2057
done	5001	1976

prune835.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.5 (* (pow x 2) n))
0.8b	(/ (- (log x)) (pow n 2))
2.1b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
8.7b	(* (pow x 2) n)

rewrite637.0ms

Algorithm

rewrite-expression-head

Rules

137×	`times-frac`
122×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
70×	`add-cube-cbrt`
46×	`unpow-prod-down`
38×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
29×	`add-exp-log`
26×	`associate-r`
25×	`pow1`
21×	`associate-l`
19×	`log-pow`
18×	`add-cbrt-cube` `unpow2` `sqr-pow`
15×	`associate-/l*` `difference-of-squares`
9×	`neg-mul-1` `associate-/r*`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
5×	`distribute-lft-out--`
4×	`cbrt-undiv` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`neg-sub0` `distribute-rgt-in` `frac-times` `pow-to-exp` `distribute-lft-in` `div-sub` `associate-*r/` `pow-exp`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`distribute-frac-neg` `pow-prod-down` `associate-*l/`

Counts

4 → 246

Calls

4 calls:

18.0ms	(/ 0.5 (* (pow x 2) n))
34.0ms	(/ (- (log x)) (pow n 2))
548.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
23.0ms	(* (pow x 2) n)

series392.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 0.5 (* (pow x 2) n))
115.0ms	(/ (- (log x)) (pow n 2))
215.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
26.0ms	(* (pow x 2) n)

simplify2.1s

Counts

258 → 258

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	405	3726
1	957	3385
2	2879	2963
done	5000	2961

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.7b

regimes453.0ms

Accuracy

81.1% (1.7b remaining)

Error of 22.3b against oracle of 20.6b and baseline of 29.4b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	96
1	46	67
done	46	67

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.8s	3159×	body	1280	valid
1.2s	1125×	body	10240	exit
928.0ms	1602×	body	640	valid
771.0ms	882×	body	320	valid
613.0ms	635×	body	1280	nan
522.0ms	4813×	body	80	valid
459.0ms	662×	body	640	nan
370.0ms	5108×	body	80	nan
111.0ms	337×	body	320	nan
107.0ms	444×	body	160	valid
37.0ms	187×	body	160	nan