Details

sample183.0ms

Algorithm

intervals

Results

51.0ms	90×	body	1280	valid
29.0ms	67×	body	640	valid
25.0ms	39×	body	10240	exit
13.0ms	172×	body	80	valid
9.0ms	14×	body	1280	nan
9.0ms	31×	body	320	valid
8.0ms	21×	body	640	nan
8.0ms	169×	body	80	nan
3.0ms	11×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	5×	body	160	nan

simplify3.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize30.0ms

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)))

rewrite151.0ms

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:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
7.0ms	(pow x (/ 1.0 n))
130.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series683.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(pow (+ x 1.0) (/ 1.0 n))
82.0ms	(pow x (/ 1.0 n))
430.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.4s

Counts

88 → 88

Iterations

Useful iterations: 3 (982.0ms)

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

prune798.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow x (/ 1.0 n)) 3)
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)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
44×	`unpow-prod-down`
29×	`pow-unpow` `*-un-lft-identity`
27×	`difference-of-squares`
25×	`add-cube-cbrt`
24×	`cbrt-prod`
23×	`sqr-pow`
18×	`times-frac`
16×	`cube-prod`
8×	`add-exp-log`
6×	`pow1` `pow-exp` `add-log-exp`
5×	`add-cbrt-cube`
4×	`pow-to-exp`
3×	`pow-pow`
2×	`div-inv`
1×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 128

Calls

4 calls:

9.0ms	(pow (pow x (/ 1.0 n)) 3)
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
110.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(pow (pow x (/ 1.0 n)) 3)
226.0ms	(pow (+ x 1.0) (/ 1.0 n))
70.0ms	(pow x (/ 1.0 n))
414.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify1.3s

Counts

140 → 140

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	261	2602
1	665	2235
2	1837	2187
done	5000	2175

prune584.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.9b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* 1.0 (log x)) (* x (pow n 2)))
1.8b	(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
8.5b	(* x (pow n 2))
8.7b	(* (pow x 2) n)

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
31×	`add-sqr-sqrt`
20×	`add-cbrt-cube`
16×	`prod-exp`
12×	`*-un-lft-identity`
11×	`associate-r` `associate-l`
10×	`add-cube-cbrt`
8×	`unpow-prod-down` `div-exp` `unswap-sqr`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `pow-to-exp` `times-frac` `pow-exp` `unpow2` `sqr-pow`
3×	`difference-of-squares`
2×	`*-commutative`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `associate-/r` `frac-sub` `flip--` `div-inv` `associate-/l` `distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

17.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
95.0ms	(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
13.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

series268.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (* 1.0 (log x)) (* x (pow n 2)))
93.0ms	(- (/ (/ 1.0 n) x) (/ 0.5 (* (pow x 2) n)))
42.0ms	(* x (pow n 2))
34.0ms	(* (pow x 2) n)

simplify1.3s

Counts

108 → 108

Iterations

Useful iterations: 2 (502.0ms)

Iter	Nodes	Cost
0	190	1346
1	477	1257
2	1791	1067
done	5000	1067

prune484.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 22.8b

localize43.0ms

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)

rewrite593.0ms

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:

9.0ms	(/ 0.5 (* (pow x 2) n))
19.0ms	(/ (- (log x)) (pow n 2))
517.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
36.0ms	(* (pow x 2) n)

series428.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 0.5 (* (pow x 2) n))
144.0ms	(/ (- (log x)) (pow n 2))
214.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
30.0ms	(* (pow x 2) n)

simplify2.0s

Counts

258 → 258

Iterations

Useful iterations: done (2.0s)

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

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.8b

regimes343.0ms

Accuracy

81.5% (1.6b remaining)

Error of 22.3b against oracle of 20.7b and baseline of 29.4b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	31	68
1	39	53
done	39	53

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.4s	3159×	body	1280	valid
1.0s	1125×	body	10240	exit
933.0ms	1602×	body	640	valid
633.0ms	4813×	body	80	valid
582.0ms	635×	body	1280	nan
431.0ms	662×	body	640	nan
419.0ms	5108×	body	80	nan
361.0ms	882×	body	320	valid
118.0ms	337×	body	320	nan
100.0ms	444×	body	160	valid
36.0ms	187×	body	160	nan