Details

sample56.0ms

Algorithm

intervals

Results

23.0ms	387×	body	80	valid
7.0ms	143×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2078
5	627
4	203
3	85
2	45
1	24
0	12

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* k (+ k 10.0)) 1.0)
0.0b	(* k (+ k 10.0))
0.5b	(/ (pow k m) (+ (* k (+ k 10.0)) 1.0))
2.2b	(* (/ (pow k m) (+ (* k (+ k 10.0)) 1.0)) a)

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

9.0ms	(+ (* k (+ k 10.0)) 1.0)
21.0ms	(* k (+ k 10.0))
38.0ms	(/ (pow k m) (+ (* k (+ k 10.0)) 1.0))
72.0ms	(* (/ (pow k m) (+ (* k (+ k 10.0)) 1.0)) a)

series322.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (* k (+ k 10.0)) 1.0)
63.0ms	(* k (+ k 10.0))
95.0ms	(/ (pow k m) (+ (* k (+ k 10.0)) 1.0))
141.0ms	(* (/ (pow k m) (+ (* k (+ k 10.0)) 1.0)) a)

simplify1.9s

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
2	2247
1	656
0	249

prune933.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (sqrt (+ (* k (+ k 10.0)) 1.0))) (* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a))
0.1b	(* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a)
14.8b	(sqrt (+ (* k (+ k 10.0)) 1.0))
14.8b	(sqrt (+ (* k (+ k 10.0)) 1.0))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-exp-log`
72×	`associate-l`
67×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
40×	`prod-exp`
39×	`sqrt-prod`
30×	`add-cbrt-cube`
25×	`div-exp`
20×	`unpow-prod-down`
13×	`pow1`
12×	`cbrt-unprod`
8×	`sqrt-div` `sqr-pow`
7×	`unswap-sqr`
6×	`cbrt-undiv`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`flip3-+` `associate-r` `pow-prod-down` `associate-*l/` `associate-/r/` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`
1×	`frac-times` `associate-*r/`

Counts

4 → 168

Calls

4 calls:

156.0ms	(* (/ 1 (sqrt (+ (* k (+ k 10.0)) 1.0))) (* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a))
56.0ms	(* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a)
17.0ms	(sqrt (+ (* k (+ k 10.0)) 1.0))
26.0ms	(sqrt (+ (* k (+ k 10.0)) 1.0))

series554.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (/ 1 (sqrt (+ (* k (+ k 10.0)) 1.0))) (* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a))
271.0ms	(* (/ (pow k m) (sqrt (+ (* k (+ k 10.0)) 1.0))) a)
66.0ms	(sqrt (+ (* k (+ k 10.0)) 1.0))
65.0ms	(sqrt (+ (* k (+ k 10.0)) 1.0))

simplify2.1s

Counts

180 → 180

Iterations

Iter	Nodes
done	5005
2	2625
1	795
0	294

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (exp (* m (+ 0 (log k)))) (* k k))
4.7b	(/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k))
8.2b	(/ a (* k k))
11.1b	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

64×	`associate-*l/`
33×	`frac-times` `associate-*r/` `frac-sub`
31×	`frac-add`
26×	`add-cbrt-cube`
22×	`add-exp-log`
9×	`times-frac` `associate-/l*` `add-log-exp`
8×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1` `exp-sum` `sub-div`
3×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip-+` `div-inv`
2×	`distribute-rgt-in` `distribute-lft-in` `diff-log`
1×	`sum-log` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 118

Calls

4 calls:

22.0ms	(/ (exp (* m (+ 0 (log k)))) (* k k))
27.0ms	(/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k))
12.0ms	(/ a (* k k))
1.1s	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (exp (* m (+ 0 (log k)))) (* k k))
72.0ms	(/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k))
40.0ms	(/ a (* k k))
252.0ms	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))

simplify3.7s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	4815
1	1072
0	358

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize184.0ms

Local error

Found 4 expressions with local error:

11.1b	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
14.5b	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
14.5b	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
14.5b	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/`
132×	`frac-times` `associate-*r/` `frac-sub`
124×	`frac-add`
117×	`cbrt-div`
16×	`sub-div`
12×	`flip3-+` `flip-+`
9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`pow1/3`
2×	`diff-log`
1×	`sum-log` `sub-neg` `associate--l+`

Counts

4 → 201

Calls

4 calls:

1.3s	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
527.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
423.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
500.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))

series1.6s

Counts

4 → 12

Calls

4 calls:

237.0ms	(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
480.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
486.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))
435.0ms	(cbrt (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))))

simplify3.2s

Counts

213 → 213

Iterations

Iter	Nodes
done	5007
2	3496
1	952
0	364

prune2.6s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

98.3% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch95.0ms

Steps

Iters	Range		Point
10	136722479363809.36	1.9717371469647825e+28	7.623829945060762e+19

simplify8.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	11962×	body	80	valid
673.0ms	4225×	body	80	nan