Details

sample94.0ms

Algorithm

intervals

Results

35.0ms	369×	body	80	valid
18.0ms	133×	body	80	nan

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	48	13
3	95	13
4	239	13
5	718	13
6	2745	13
done	5000	13

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.4b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
10×	`add-log-exp`
8×	`add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `sum-log`
3×	`pow1` `flip3-+` `times-frac` `prod-exp` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `+-commutative` `associate-/r/`
1×	`pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

3 → 49

Calls

3 calls:

5.0ms	(+ 1.0 (* 10.0 k))
29.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
45.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(+ 1.0 (* 10.0 k))
33.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
178.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts

58 → 58

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	141	1027
1	399	876
2	1441	782
done	5000	737

prune200.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.2b	(/ 1 (+ 1.0 (* k (+ 10.0 k))))
1.2b	(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-exp-log`
29×	`prod-exp`
22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`associate-r` `add-cbrt-cube`
18×	`times-frac`
10×	`div-exp`
8×	`pow1`
7×	`cbrt-unprod`
5×	`rec-exp` `1-exp`
4×	`pow-to-exp` `associate-l` `pow-exp` `associate-/r/`
3×	`cbrt-undiv` `flip3-+` `associate-r/` `associate-/r` `flip-+` `associate-/l*` `add-log-exp`
2×	`pow-prod-down` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `un-div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

3 → 103

Calls

3 calls:

27.0ms	(* k (+ 10.0 k))
10.0ms	(/ 1 (+ 1.0 (* k (+ 10.0 k))))
56.0ms	(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

series309.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* k (+ 10.0 k))
43.0ms	(/ 1 (+ 1.0 (* k (+ 10.0 k))))
199.0ms	(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	203	1785
1	548	1558
2	1821	1370
done	5001	1337

prune270.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
1.2b	(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
13.2b	(sqrt (+ 1.0 (* (+ 10.0 k) k)))
13.2b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

522×	`times-frac`
276×	`add-sqr-sqrt`
274×	`add-cube-cbrt` `*-un-lft-identity`
270×	`sqrt-prod`
150×	`associate-r`
83×	`add-exp-log`
35×	`prod-exp`
34×	`sqrt-div`
30×	`div-exp` `associate-/r/` `add-cbrt-cube`
24×	`associate-/l*`
17×	`flip3-+` `flip-+`
15×	`div-inv`
9×	`cbrt-undiv` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r*`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-r/` `associate-l` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 410

Calls

4 calls:

32.0ms	(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
85.0ms	(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
5.0ms	(sqrt (+ 1.0 (* (+ 10.0 k) k)))
5.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
183.0ms	(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
58.0ms	(sqrt (+ 1.0 (* (+ 10.0 k) k)))
70.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.1s

Counts

422 → 422

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	529	14029
1	1472	11117
2	3560	10117
done	5002	9754

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.0b	(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
13.2b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
13.2b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-exp-log`
40×	`add-sqr-sqrt`
33×	`prod-exp`
28×	`-un-lft-identity` `times-frac` `associate-r*`
27×	`add-cbrt-cube`
26×	`div-exp`
24×	`add-cube-cbrt`
20×	`sqrt-prod`
15×	`associate-l`
10×	`pow1`
9×	`cbrt-unprod`
8×	`sqrt-div`
7×	`cbrt-undiv`
6×	`unswap-sqr`
5×	`rec-exp` `flip3-+` `1-exp` `flip-+`
4×	`pow-to-exp` `pow-exp` `associate-/r/` `add-log-exp`
3×	`associate-*r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*l/` `un-div-inv` `distribute-lft-out`

Counts

4 → 133

Calls

4 calls:

20.0ms	(* k (+ 10.0 k))
100.0ms	(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
5.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
6.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* k (+ 10.0 k))
158.0ms	(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
65.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
72.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.8s

Counts

145 → 145

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	260	3422
1	718	2991
2	2439	2287
done	5002	2272

prune563.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes92.0ms

Accuracy

97.3% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.9b

bsearch459.0ms

Steps

Iters	Range		Point
8	6.078647819315964e+130	2.9949035539067785e+135	4.309780576654703e+132

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	61
1	47	61
done	47	61

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	11910×	body	80	valid
398.0ms	4225×	body	80	nan