Details

sample289.0ms

Algorithm

intervals

Results

98.0ms	85×	body	640	valid
90.0ms	93×	body	1280	valid
44.0ms	269×	body	80	valid
22.0ms	46×	body	320	valid
7.0ms	21×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
9	2396
8	1697
7	948
6	527
5	277
4	181
3	78
2	39
1	23
0	14

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
5.7b	(- (exp l) (exp (- l)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`sub-neg` `flip3--` `insert-posit16` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

47.0ms	(* J (- (exp l) (exp (- l))))
69.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
12.0ms	(- (exp l) (exp (- l)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(* J (- (exp l) (exp (- l))))
122.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
40.0ms	(- (exp l) (exp (- l)))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
3	3009
2	737
1	274
0	114

prune455.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2))) U)
0.1b	(* (pow l 5) 1/60)
0.1b	(* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2)))
0.2b	(* 1/3 (* l l))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
14×	`pow1`
11×	`associate-l`
9×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
7×	`associate-r` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 79

Calls

4 calls:

67.0ms	(+ (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2))) U)
17.0ms	(* (pow l 5) 1/60)
54.0ms	(* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2)))
25.0ms	(* 1/3 (* l l))

series886.0ms

Counts

4 → 12

Calls

4 calls:

533.0ms	(+ (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2))) U)
71.0ms	(* (pow l 5) 1/60)
230.0ms	(* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2)))
52.0ms	(* 1/3 (* l l))

simplify8.2s

Counts

91 → 91

Iterations

Iter	Nodes
3	11382
2	1835
1	470
0	168

prune782.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* l l) (* l l))
0.1b	(* J (* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l))))))
0.1b	(* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
0.1b	(* 1/3 (* (* l l) l))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

131×	`pow1`
36×	`pow-prod-up`
33×	`pow-prod-down`
32×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus` `prod-exp` `cbrt-unprod`
13×	`pow2`
10×	`add-sqr-sqrt` `associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `associate-*r/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`swap-sqr`

Counts

4 → 134

Calls

4 calls:

32.0ms	(* (* l l) (* l l))
939.0ms	(* J (* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l))))))
946.0ms	(* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
57.0ms	(* 1/3 (* (* l l) l))

series691.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* l l) (* l l))
362.0ms	(* J (* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l))))))
233.0ms	(* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
46.0ms	(* 1/3 (* (* l l) l))

simplify9.8s

Counts

146 → 146

Iterations

Iter	Nodes
3	12756
2	1959
1	516
0	187

prune667.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J (cos (/ K 2))) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
0.1b	(* J (cos (/ K 2)))
0.1b	(* (* l l) (* l l))
0.1b	(* 1/3 (* (* l l) l))

rewrite791.0ms

Algorithm

rewrite-expression-head

Rules

131×	`pow1`
36×	`pow-prod-up`
33×	`pow-prod-down`
32×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus` `prod-exp` `cbrt-unprod`
13×	`pow2`
10×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 128

Calls

4 calls:

718.0ms	(* (* J (cos (/ K 2))) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
7.0ms	(* J (cos (/ K 2)))
28.0ms	(* (* l l) (* l l))
36.0ms	(* 1/3 (* (* l l) l))

series527.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (* J (cos (/ K 2))) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
62.0ms	(* J (cos (/ K 2)))
40.0ms	(* (* l l) (* l l))
41.0ms	(* 1/3 (* (* l l) l))

simplify7.5s

Counts

140 → 140

Iterations

Iter	Nodes
3	10221
2	1705
1	459
0	166

prune643.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes653.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	31
1	31
0	21

end0.0ms

sample10.3s

Algorithm

intervals

Results

4.0s	2669×	body	1280	valid
2.8s	2611×	body	640	valid
1.7s	8319×	body	80	valid
959.0ms	1465×	body	320	valid
328.0ms	749×	body	160	valid