Details

sample94.0ms

Algorithm

intervals

Results

50.0ms	371×	body	80	valid
10.0ms	122×	body	80	nan

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	2353
5	632
4	203
3	85
2	45
1	24
0	12

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

29.0ms	(* a (pow k m))
47.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
68.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series391.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(* a (pow k m))
36.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
235.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify2.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1402
1	411
0	155

prune639.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ k 10.0))
0.2b	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
2.0b	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
31×	`associate-r`
22×	`unpow-prod-down`
20×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`pow1` `associate-/l*`
6×	`div-exp` `associate-l`
5×	`prod-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3-+` `associate-r/` `associate-/r` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-prod-down` `pow-exp` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

40.0ms	(* k (+ k 10.0))
27.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
73.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

series441.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* k (+ k 10.0))
124.0ms	(/ (pow k m) (+ 1.0 (* k (+ k 10.0))))
229.0ms	(* a (/ (pow k m) (+ 1.0 (* k (+ k 10.0)))))

simplify3.1s

Counts

129 → 129

Iterations

Iter	Nodes
done	5010
2	2224
1	638
0	240

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
14.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.0b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
66×	`sqrt-prod`
55×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `sqrt-div`
16×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`associate-/l*`
11×	`flip3-+` `flip-+`
9×	`div-exp` `add-log-exp`
8×	`div-inv`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
3×	`prod-exp` `sum-log`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

46.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
151.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
52.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
234.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
102.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
86.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify3.5s

Counts

166 → 166

Iterations

Iter	Nodes
done	5000
2	2649
1	719
0	280

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(* k (+ k 10.0))
0.2b	(/ 1 (/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m))))
1.9b	(/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
36×	`times-frac`
34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
26×	`div-exp`
22×	`add-cbrt-cube`
16×	`prod-exp`
11×	`associate-r`
8×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`associate-l` `div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`unpow-prod-down` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `flip3-+` `associate-r/` `clear-num` `-commutative` `flip-+` `associate-/l/` `sqr-pow`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `associate-/r/` `distribute-lft-out` `inv-pow`

Counts

4 → 135

Calls

4 calls:

23.0ms	(* a (pow k m))
42.0ms	(* k (+ k 10.0))
68.0ms	(/ 1 (/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m))))
98.0ms	(/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* a (pow k m))
96.0ms	(* k (+ k 10.0))
211.0ms	(/ 1 (/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m))))
235.0ms	(/ (+ (* k (+ k 10.0)) 1.0) (* a (pow k m)))

simplify3.5s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	2559
1	713
0	264

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes312.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch122.0ms

Steps

Iters	Range		Point
9	3.232642262437057e+131	4.4669207121361405e+139	4.5006258076783667e+133

simplify11.0ms

Iterations

Iter	Nodes
done	35
1	35
0	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.4s	11787×	body	80	valid
1.2s	4210×	body	80	nan