Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	382×	body	80	valid
4.0ms	132×	body	80	nan

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	47	13
3	91	13
4	228	13
5	695	13
6	2360	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow k m))
2.9b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
6.0ms	(* a (pow k m))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
57.0ms	(* a (pow k m))
121.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify712.0ms

Counts

86 → 86

Iterations

Useful iterations: done (709.0ms)

Iter	Nodes	Cost
0	171	1264
1	455	1102
2	1497	988
done	5000	984

prune226.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.1b	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
134×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
48×	`associate-r`
45×	`unpow-prod-down`
33×	`add-exp-log`
24×	`associate-l`
21×	`unswap-sqr`
19×	`sqr-pow`
18×	`add-cbrt-cube`
13×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
7×	`associate-/l*`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 218

Calls

4 calls:

10.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
51.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
118.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
247.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
47.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.3s

Counts

230 → 230

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	326	6183
1	895	5790
2	3018	5279
done	5001	5229

prune598.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m))
0.0b	(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
38×	`add-exp-log`
30×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l` `sqrt-prod`
18×	`add-cbrt-cube`
13×	`div-exp`
12×	`prod-exp`
9×	`unswap-sqr`
8×	`sqrt-div`
7×	`associate-r`
6×	`pow1` `unpow-prod-down` `associate-/r*`
5×	`cbrt-undiv`
4×	`pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp` `sqr-pow`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `div-inv`
1×	`frac-2neg` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 123

Calls

4 calls:

24.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m))
13.0ms	(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m))
113.0ms	(/ (* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (pow k m)) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
51.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
48.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: 2 (367.0ms)

Iter	Nodes	Cost
0	240	3018
1	640	2813
2	2338	2400
done	5000	2400

prune402.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
18.3b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
52×	`add-sqr-sqrt`
35×	`sqrt-pow1`
30×	`pow1` `sqrt-div`
19×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`rem-sqrt-square`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

26.0ms	(* (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series198.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))) (sqrt (sqrt (+ 1.0 (* k (+ 10.0 k))))))
46.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
52.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
47.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify1.6s

Counts

140 → 140

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	131	3018
1	260	1961
2	754	1833
3	2861	1767
done	5000	1765

prune362.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.8b

regimes76.0ms

Accuracy

0% (0.1b remaining)

Error of 2.1b against oracle of 2.0b and baseline of 2.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	17	23
done	17	23

end0.0ms

sample984.0ms

Algorithm

intervals

Results

490.0ms	11915×	body	80	valid
149.0ms	4312×	body	80	nan