Details

sample96.0ms

Algorithm

intervals

Results

38.0ms	387×	body	80	valid
15.0ms	174×	body	80	nan

simplify1.8s

Counts: 1 → 1

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.3b	(* a (pow k m))
2.6b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite127.0ms

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:

15.0ms	(+ 1.0 (* 10.0 k))
26.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
17.0ms	(* a (pow k m))
67.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ 1.0 (* 10.0 k))
23.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
76.0ms	(* a (pow k m))
149.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify963.0ms

Counts: 86 → 86

prune318.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0b	(* a (pow k (/ m 2)))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.6b	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

31.0ms	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
24.0ms	(* a (pow k (/ m 2)))
26.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
71.0ms	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
112.0ms	(* a (pow k (/ m 2)))
29.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
216.0ms	(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.1s

Counts: 115 → 115

prune487.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 120

Calls

3 calls:

29.0ms	(* k (+ 10.0 k))
23.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
111.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series293.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* k (+ 10.0 k))
81.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
137.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify1.3s

Counts: 129 → 129

prune487.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.1b	(/ 1 (/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2)))))
0.2b	(/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2))))
4.5b	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a)

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

1073×	`times-frac`
496×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
198×	`unpow-prod-down`
105×	`associate-/r*`
68×	`add-exp-log`
66×	`sqr-pow`
51×	`div-exp`
43×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/l*`
10×	`cbrt-undiv`
9×	`add-log-exp`
8×	`pow-to-exp` `pow-exp`
7×	`rec-exp` `1-exp`
5×	`pow1`
3×	`frac-2neg` `clear-num` `sum-log` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 592

Calls

4 calls:

37.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
93.0ms	(/ 1 (/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2)))))
120.0ms	(/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2))))
109.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a)

series430.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
147.0ms	(/ 1 (/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2)))))
183.0ms	(/ (/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a) (pow k (* 2 (/ m 2))))
77.0ms	(/ (+ (+ 1.0 (* 10.0 k)) (* k k)) a)

simplify1.2s

Counts: 604 → 604

prune2.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 2.6b

regimes92.0ms

Accuracy

-197.6% (0.2b remaining)

Error of 2.1b against oracle of 1.9b and baseline of 2.0b

bsearch0.0ms

simplify1.6s

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	11864×	body	80	valid
492.0ms	4162×	body	80	nan