Details

sample90.0ms

Algorithm

intervals

Results

55.0ms	369×	body	80	valid
14.0ms	106×	body	80	nan

simplify8.9s

Counts

1 → 1

Iterations

Iter	Nodes
7	7970
6	1954
5	624
4	202
3	85
2	45
1	24
0	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow k m) a)
0.0b	(* k (+ k 10))
2.7b	(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

7.0ms	(* (pow k m) a)
12.0ms	(* k (+ k 10))
17.0ms	(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

series297.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(* (pow k m) a)
61.0ms	(* k (+ k 10))
121.0ms	(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

simplify4.6s

Counts

82 → 82

Iterations

Iter	Nodes
3	7731
2	1415
1	434
0	163

prune909.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* k (+ k 10))
0.1b	(/ (/ (* (pow k m) a) (sqrt (+ (* k (+ k 10)) 1))) (sqrt (+ (* k (+ k 10)) 1)))
13.8b	(sqrt (+ (* k (+ k 10)) 1))
13.8b	(sqrt (+ (* k (+ k 10)) 1))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
66×	`sqrt-prod`
59×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
22×	`add-exp-log`
20×	`sqrt-div`
16×	`associate-/r/`
15×	`add-cbrt-cube`
12×	`associate-/l*`
11×	`flip3-+` `flip-+`
9×	`div-exp`
8×	`pow1` `div-inv`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`associate-r` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `cbrt-unprod`
1×	`distribute-rgt-in` `pow-to-exp` `clear-num` `frac-2neg` `distribute-lft-in` `pow-prod-down` `pow-exp` `*-commutative` `distribute-lft-out` `unswap-sqr` `associate-/l/`

Counts

4 → 164

Calls

4 calls:

24.0ms	(* k (+ k 10))
42.0ms	(/ (/ (* (pow k m) a) (sqrt (+ (* k (+ k 10)) 1))) (sqrt (+ (* k (+ k 10)) 1)))
9.0ms	(sqrt (+ (* k (+ k 10)) 1))
14.0ms	(sqrt (+ (* k (+ k 10)) 1))

series238.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* k (+ k 10))
115.0ms	(/ (/ (* (pow k m) a) (sqrt (+ (* k (+ k 10)) 1))) (sqrt (+ (* k (+ k 10)) 1)))
31.0ms	(sqrt (+ (* k (+ k 10)) 1))
34.0ms	(sqrt (+ (* k (+ k 10)) 1))

simplify833.0ms

Counts

176 → 176

Iterations

Iter	Nodes
2	2285
1	734
0	286

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

13.8b	(sqrt (+ (* k (+ k 10)) 1))
14.3b	(cbrt (+ (* k (+ k 10)) 1))
14.3b	(cbrt (+ (* k (+ k 10)) 1))
14.3b	(cbrt (+ (* k (+ k 10)) 1))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

9.0ms	(sqrt (+ (* k (+ k 10)) 1))
5.0ms	(cbrt (+ (* k (+ k 10)) 1))
9.0ms	(cbrt (+ (* k (+ k 10)) 1))
11.0ms	(cbrt (+ (* k (+ k 10)) 1))

series236.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(sqrt (+ (* k (+ k 10)) 1))
64.0ms	(cbrt (+ (* k (+ k 10)) 1))
66.0ms	(cbrt (+ (* k (+ k 10)) 1))
48.0ms	(cbrt (+ (* k (+ k 10)) 1))

simplify3.8s

Counts

66 → 66

Iterations

Iter	Nodes
4	5619
3	1832
2	503
1	180
0	82

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a))
7.4b	(+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k))))
8.4b	(/ a (* k k))
9.9b	(+ (/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a)) (+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-cbrt-cube`
59×	`add-exp-log`
30×	`associate-*r/`
29×	`frac-add`
24×	`cbrt-undiv` `div-exp`
23×	`prod-exp` `cbrt-unprod`
16×	`times-frac`
12×	`frac-times` `-un-lft-identity` `associate-l/`
11×	`add-log-exp`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`associate-/r*`
4×	`pow1` `sum-log` `div-inv` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `clear-num` `frac-2neg`
1×	`associate-+r+` `associate-/r/` `distribute-lft-out`

Counts

4 → 116

Calls

4 calls:

22.0ms	(/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a))
22.0ms	(+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k))))
13.0ms	(/ a (* k k))
77.0ms	(+ (/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a)) (+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k)))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a))
153.0ms	(+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k))))
37.0ms	(/ a (* k k))
240.0ms	(+ (/ (* 99 (exp (* (log k) m))) (/ (* (* k k) (* k k)) a)) (+ (* (/ a k) (/ (exp (* (log k) m)) k)) (* -10 (* (/ a (* k k)) (/ (exp (* (log k) m)) k)))))

simplify2.5s

Counts

128 → 128

Iterations

Iter	Nodes
2	4709
1	1110
0	321

prune2.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

98.5% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch76.0ms

Steps

Iters	Range		Point
6	9.545690680202222e+129	4.384054805801543e+130	3.641563002348689e+130

simplify13.0ms

Iterations

Iter	Nodes
2	43
1	43
0	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.1s	12018×	body	80	valid
564.0ms	4190×	body	80	nan