Details

sample258.0ms

Algorithm

intervals

Results

80.0ms	90×	body	1280	valid
40.0ms	67×	body	640	valid
27.0ms	39×	body	10240	exit
21.0ms	172×	body	80	valid
13.0ms	21×	body	640	nan
12.0ms	169×	body	80	nan
12.0ms	31×	body	320	valid
10.0ms	14×	body	1280	nan
4.0ms	11×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	5×	body	160	nan

simplify2.5s

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize11.0ms

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)))

rewrite157.0ms

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:

22.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(pow x (/ 1.0 n))
120.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series723.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(pow (+ x 1.0) (/ 1.0 n))
88.0ms	(pow x (/ 1.0 n))
435.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify706.0ms

Counts: 88 → 88

prune417.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.9b

localize25.0ms

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)))

rewrite159.0ms

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:

55.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
21.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
10.0ms	(pow x (/ 1.0 n))
65.0ms	(- (* (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)))

series2.2s

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
501.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
82.0ms	(pow x (/ 1.0 n))
1.4s	(- (* (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

prune733.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.7b

localize53.0ms

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

rewrite190.0ms

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:

65.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
12.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
5.0ms	(pow x (/ 1.0 n))
100.0ms	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series2.1s

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
432.0ms	(pow (cbrt (+ x 1.0)) (/ 1.0 n))
91.0ms	(pow x (/ 1.0 n))
1.3s	(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify1.4s

Counts: 136 → 136

prune822.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* (log x) 1.0) (* x (pow n 2)))
1.8b	(- (/ (/ 1.0 n) x) (- (/ (/ (/ 1.0 2.0) n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
8.5b	(/ (/ (/ 1.0 2.0) n) (pow x 2))
8.5b	(* x (pow n 2))

rewrite987.0ms

Algorithm

rewrite-expression-head

Rules

942×	`times-frac`
425×	`add-sqr-sqrt`
415×	`*-un-lft-identity`
410×	`add-cube-cbrt`
136×	`unpow-prod-down`
57×	`add-exp-log`
46×	`unpow2` `sqr-pow`
44×	`associate-/l*`
38×	`div-inv`
27×	`add-cbrt-cube`
26×	`div-exp`
13×	`prod-exp`
10×	`cbrt-undiv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
6×	`pow-to-exp` `pow-exp`
5×	`cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 494

Calls

4 calls:

32.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
838.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ (/ 1.0 2.0) n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
43.0ms	(/ (/ (/ 1.0 2.0) n) (pow x 2))
13.0ms	(* x (pow n 2))

series296.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
95.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ (/ 1.0 2.0) n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
45.0ms	(/ (/ (/ 1.0 2.0) n) (pow x 2))
44.0ms	(* x (pow n 2))

simplify1.1s

Counts: 506 → 506

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.7b

regimes482.0ms

Accuracy

83.5% (1.5b remaining)

Error of 22.1b against oracle of 20.6b and baseline of 29.5b

bsearch279.0ms

Steps

Iters	Range		Point
5	65877241274.64672	241918210538.82648	104589929251.33272
10	-8534861749055764.0	-1.8687997873074387	-22082318.544752534

simplify1.3s

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.5s	3159×	body	1280	valid
1.8s	1602×	body	640	valid
978.0ms	1125×	body	10240	exit
574.0ms	4813×	body	80	valid
485.0ms	635×	body	1280	nan
420.0ms	5108×	body	80	nan
396.0ms	662×	body	640	nan
309.0ms	882×	body	320	valid
152.0ms	337×	body	320	nan
107.0ms	444×	body	160	valid
35.0ms	187×	body	160	nan