Details

sample175.0ms

Algorithm

intervals

Results

91.0ms	78×	body	1280	valid
29.0ms	46×	body	640	valid
19.0ms	22×	body	2560	valid
14.0ms	34×	body	320	valid
7.0ms	67×	body	80	valid
2.0ms	9×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize12.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1)))
2.3b	(log (+ x (sqrt (+ (* x x) 1))))
16.2b	(sqrt (+ (* x x) 1))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
4×	`log-prod` `add-exp-log` `distribute-lft-out`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `associate-l` `log-pow`

Counts

3 → 47

Calls

3 calls:

57.0ms	(+ x (sqrt (+ (* x x) 1)))
70.0ms	(log (+ x (sqrt (+ (* x x) 1))))
39.0ms	(sqrt (+ (* x x) 1))

series222.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ x (sqrt (+ (* x x) 1)))
119.0ms	(log (+ x (sqrt (+ (* x x) 1))))
32.0ms	(sqrt (+ (* x x) 1))

simplify1.8s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
3	1978
2	707
1	273
0	121

prune315.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 1/6)
19.4b	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

84×	`associate-l`
67×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
34×	`pow1`
29×	`unswap-sqr`
23×	`add-exp-log`
22×	`associate-r`
21×	`add-cube-cbrt`
20×	`add-cbrt-cube`
12×	`prod-exp`
10×	`pow-prod-down` `*-commutative` `cbrt-unprod` `distribute-lft-out`
9×	`swap-sqr` `add-log-exp`
8×	`distribute-lft-out--`
6×	`pow-plus` `pow-prod-up`
4×	`unpow-prod-down` `insert-posit16`
2×	`pow2` `associate-+l+` `sum-log` `pow3` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sub-neg` `flip3-+` `diff-log` `pow-exp` `associate-+l-` `flip-+`

Counts

4 → 156

Calls

4 calls:

28.0ms	(* 3/40 (pow x 5))
55.0ms	(* (* x x) x)
171.0ms	(* (* (* x x) x) 1/6)
1.1s	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 3/40 (pow x 5))
50.0ms	(* (* x x) x)
53.0ms	(* (* (* x x) x) 1/6)
72.0ms	(+ (- x (* (* (* x x) x) 1/6)) (* 3/40 (pow x 5)))

simplify1.3s

Counts

168 → 168

Iterations

Iter	Nodes
done	5000
2	1284
1	458
0	167

prune470.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1/16 (pow x 5))
0.3b	(/ 1/8 (* (* x x) x))
10.7b	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
17.8b	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

8416×	`frac-sub`
7387×	`associate-/r*`
4753×	`add-sqr-sqrt`
3998×	`log-div`
3063×	`*-un-lft-identity`
3026×	`add-cube-cbrt`
2748×	`associate-/l*`
2418×	`associate-l`
1039×	`unpow-prod-down`
962×	`unswap-sqr`
916×	`clear-num` `frac-2neg`
804×	`associate-r`
540×	`swap-sqr`
406×	`*-commutative`
351×	`sqr-pow`
166×	`times-frac`
30×	`difference-of-squares`
19×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`distribute-lft-out--`
11×	`flip3--` `flip--`
10×	`log-prod`
6×	`div-exp` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `insert-posit16`
3×	`prod-exp` `cbrt-unprod`
2×	`div-inv`
1×	`pow-to-exp` `sub-neg` `diff-log` `rem-log-exp` `pow-exp` `log-pow`

Counts

4 → 4683

Calls

4 calls:

15.0ms	(/ 1/16 (pow x 5))
59.0ms	(/ 1/8 (* (* x x) x))
1.5s	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
308.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ 1/16 (pow x 5))
43.0ms	(/ 1/8 (* (* x x) x))
118.0ms	(log (- (/ -1/2 x) (- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))))
171.0ms	(- (/ 1/16 (pow x 5)) (/ 1/8 (* (* x x) x)))

simplify16.1s

Counts

4695 → 4695

Iterations

Iter	Nodes
done	13571
0	13571

prune22.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
0.1b	(* (* x x) x)
0.3b	(/ 1/8 (* (* x x) x))
7.8b	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

128×	`add-sqr-sqrt`
90×	`associate-l`
86×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-cube-cbrt`
35×	`unswap-sqr`
30×	`associate-r`
28×	`associate-/r*`
24×	`pow1`
20×	`swap-sqr`
19×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`*-commutative`
13×	`add-log-exp`
10×	`distribute-lft-out`
6×	`associate-+r+` `log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod`
5×	`sum-log`
4×	`insert-posit16`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`pow2` `+-commutative` `log-div` `associate-+r-` `flip3-+` `pow3` `pow-sqr` `flip-+` `distribute-lft-out--`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `log-pow` `div-inv`

Counts

4 → 220

Calls

4 calls:

1.2s	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
33.0ms	(* (* x x) x)
64.0ms	(/ 1/8 (* (* x x) x))
1.3s	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
36.0ms	(* (* x x) x)
65.0ms	(/ 1/8 (* (* x x) x))
116.0ms	(log (+ x (+ x (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))))

simplify2.8s

Counts

232 → 232

Iterations

Iter	Nodes
done	5108
2	3152
1	799
0	287

prune645.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.5b

bsearch133.0ms

Steps

Iters	Range		Point
10	2.618543036730298e-08	12461.173664998358	0.9560728927963928
9	-101227.54480913779	-5.532094628653386e-05	-1.0682549790295666

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	32

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.1s	2293×	body	1280	valid
940.0ms	1570×	body	640	valid
673.0ms	775×	body	2560	valid
628.0ms	2096×	body	80	valid
316.0ms	824×	body	320	valid
93.0ms	442×	body	160	valid