Details

sample227.0ms

Algorithm

intervals

Results

78.0ms	93×	body	1280	valid
75.0ms	85×	body	640	valid
33.0ms	269×	body	80	valid
16.0ms	46×	body	320	valid
5.0ms	21×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2016
7	2016
6	1067
5	416
4	202
3	85
2	44
1	24
0	14

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize44.0ms

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)))

rewrite119.0ms

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:

51.0ms	(* J (- (exp l) (exp (- l))))
52.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
13.0ms	(- (exp l) (exp (- l)))

series287.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* J (- (exp l) (exp (- l))))
153.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
74.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	2003
3	2003
2	1002
1	386
0	168

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `pow-plus` `associate-r*` `pow-prod-down` `prod-exp` `pow-prod-up` `add-cube-cbrt` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`pow2` `associate-l` `pow-sqr` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `pow3` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

16.0ms	(+ (* (* J (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))) (cos (/ K 2))) U)
0.0ms	(fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))
37.0ms	(* (* l l) l)
19.0ms	(* (* J (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))) (cos (/ K 2)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(+ (* (* J (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))) (cos (/ K 2))) U)
88.0ms	(fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))
45.0ms	(* (* l l) l)
225.0ms	(* (* J (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))) (cos (/ K 2)))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	2005
3	2005
2	1126
1	328
0	135

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
16×	`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×	`pow-plus` `pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow2` `pow-sqr` `unswap-sqr`
1×	`pow3` `fma-udef`

Counts

4 → 84

Calls

4 calls:

0.0ms	(fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))
30.0ms	(* (* l l) l)
35.0ms	(* J (* (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l))) (cos (/ K 2))))
15.0ms	(* (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l))) (cos (/ K 2)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l)))
40.0ms	(* (* l l) l)
264.0ms	(* J (* (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l))) (cos (/ K 2))))
135.0ms	(* (fma 1/60 (pow l 5) (fma (* (* l l) l) 1/3 (+ l l))) (cos (/ K 2)))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	2009
3	2009
2	1099
1	306
0	135

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

18.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))
2.0ms	(cbrt (cos (/ K 2)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
166.0ms	(cbrt (cos (/ K 2)))
137.0ms	(cbrt (cos (/ K 2)))
163.0ms	(cbrt (cos (/ K 2)))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	2000
4	2000
3	805
2	349
1	160
0	75

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes595.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample9.5s

Algorithm

intervals

Results

3.5s	2669×	body	1280	valid
2.6s	2611×	body	640	valid
1.7s	8319×	body	80	valid
810.0ms	1465×	body	320	valid
298.0ms	749×	body	160	valid