Details

sample341.0ms

Algorithm

intervals

Results

113.0ms	93×	body	1280	valid
74.0ms	85×	body	640	valid
63.0ms	46×	body	320	valid
52.0ms	269×	body	80	valid
8.0ms	21×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
8	2007
7	1093
6	610
5	337
4	198
3	83
2	42
1	24
0	14

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize59.0ms

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)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

53.0ms	(* J (- (exp l) (exp (- l))))
67.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
21.0ms	(- (exp l) (exp (- l)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* J (- (exp l) (exp (- l))))
146.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
51.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
3	2627
2	915
1	366
0	168

prune580.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in`

Counts

4 → 83

Calls

4 calls:

25.0ms	(* l (+ 2 (* 1/3 (* l l))))
33.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2))) U)
25.0ms	(* (* J (fma (pow l 5) 1/60 (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2)))
17.0ms	(* 1/3 (* l l))

series738.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* l (+ 2 (* 1/3 (* l l))))
315.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2))) U)
260.0ms	(* (* J (fma (pow l 5) 1/60 (* l (+ 2 (* 1/3 (* l l)))))) (cos (/ K 2)))
30.0ms	(* 1/3 (* l l))

simplify5.0s

Counts

95 → 95

Iterations

Iter	Nodes
3	7732
2	1552
1	454
0	162

prune712.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

152×	`pow1`
75×	`pow-prod-up`
39×	`pow-plus`
37×	`add-cbrt-cube` `add-exp-log`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
19×	`pow2` `pow-sqr`
11×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
5×	`pow3`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`unswap-sqr`

Counts

4 → 140

Calls

4 calls:

15.0ms	(* (* l l) l)
78.0ms	(* (* (* l l) l) (* l l))
23.0ms	(* (fma l (fma (* l l) 1/3 2) (* (* (* (* l l) l) (* l l)) 1/60)) (* (cos (/ K 2)) J))
7.0ms	(* (cos (/ K 2)) J)

series347.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* l l) l)
92.0ms	(* (* (* l l) l) (* l l))
139.0ms	(* (fma l (fma (* l l) 1/3 2) (* (* (* (* l l) l) (* l l)) 1/60)) (* (cos (/ K 2)) J))
59.0ms	(* (cos (/ K 2)) J)

simplify1.8s

Counts

152 → 152

Iterations

Iter	Nodes
3	3673
2	1010
1	365
0	153

prune698.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* l l))
0.2b	(* 1/3 (* l l))
0.4b	(* l (sqrt (+ 2 (* 1/3 (* l l)))))
0.5b	(* (* l (sqrt (+ 2 (* 1/3 (* l l))))) (sqrt (+ 2 (* 1/3 (* l l)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
14×	`sqrt-div` `associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
7×	`flip3-+` `sqrt-prod` `flip-+`
4×	`expm1-log1p-u` `frac-times` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 103

Calls

4 calls:

16.0ms	(* 1/3 (* l l))
14.0ms	(* 1/3 (* l l))
25.0ms	(* l (sqrt (+ 2 (* 1/3 (* l l)))))
32.0ms	(* (* l (sqrt (+ 2 (* 1/3 (* l l))))) (sqrt (+ 2 (* 1/3 (* l l)))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 1/3 (* l l))
43.0ms	(* 1/3 (* l l))
220.0ms	(* l (sqrt (+ 2 (* 1/3 (* l l)))))
128.0ms	(* (* l (sqrt (+ 2 (* 1/3 (* l l))))) (sqrt (+ 2 (* 1/3 (* l l)))))

simplify3.4s

Counts

115 → 115

Iterations

Iter	Nodes
3	5805
2	1373
1	406
0	148

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes535.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	20

end0.0ms

sample10.7s

Algorithm

intervals

Results

3.8s	2669×	body	1280	valid
3.3s	2611×	body	640	valid
1.8s	8319×	body	80	valid
942.0ms	1465×	body	320	valid
365.0ms	749×	body	160	valid