Details

sample105.0ms

Algorithm

intervals

Results

32.0ms	80×	body	1280	valid
21.0ms	81×	body	640	valid
16.0ms	250×	body	80	valid
10.0ms	57×	body	320	valid
2.0ms	19×	body	160	valid

simplify16.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	45	14
3	90	14
4	189	14
5	281	14
6	358	14
7	493	14
8	646	14
9	1031	14
10	1800	14
11	2586	14
12	3243	14
13	3564	14
14	3648	14
done	3648	14

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
0.0b	(* J (- (exp l) (exp (- l))))
5.0b	(- (exp l) (exp (- l)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
51.0ms	(* J (- (exp l) (exp (- l))))
16.0ms	(- (exp l) (exp (- l)))

series275.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
59.0ms	(* J (- (exp l) (exp (- l))))
38.0ms	(- (exp l) (exp (- l)))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	162	1865
1	315	1440
2	739	1116
3	2902	950
done	5001	923

prune232.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0b	(fma 1/60 (pow l 5) (* 2 l))
0.0b	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0b	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
5×	`fma-udef`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

0.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.0ms	(fma 1/60 (pow l 5) (* 2 l))
11.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series596.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
129.0ms	(fma 1/60 (pow l 5) (* 2 l))
146.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
258.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 3 (474.0ms)

Iter	Nodes	Cost
0	97	1182
1	186	1164
2	565	1011
3	2819	997
done	5000	997

prune273.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J))
0.0b	(fma (+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)) U)
0.2b	(* 1/3 (pow l 3))
6.2b	(* (* 1/3 (pow l 3)) J)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
15×	`associate-r`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `cube-prod` `associate-l` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`pow-to-exp` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `cube-mult` `distribute-rgt-out` `fma-def` `flip3-+` `unpow3` `pow-prod-down` `sum-log` `flip-+` `fma-udef`

Counts

4 → 79

Calls

4 calls:

24.0ms	(+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J))
0.0ms	(fma (+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)) U)
12.0ms	(* 1/3 (pow l 3))
22.0ms	(* (* 1/3 (pow l 3)) J)

series303.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J))
154.0ms	(fma (+ (* (* 1/3 (pow l 3)) J) (* (fma 1/60 (pow l 5) (* 2 l)) J)) (cos (/ K 2.0)) U)
38.0ms	(* 1/3 (pow l 3))
28.0ms	(* (* 1/3 (pow l 3)) J)

simplify918.0ms

Counts

91 → 91

Iterations

Useful iterations: done (915.0ms)

Iter	Nodes	Cost
0	144	1337
1	351	1154
2	1346	1034
done	5000	1016

prune334.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
14.8b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
14.8b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
14.8b	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

14.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
6.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
3.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
3.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

347.0ms	(* (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))) (cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))))
306.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
300.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))
303.0ms	(cbrt (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))))

simplify1.0s

Counts

78 → 78

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	132	2272
1	296	2080
2	769	1843
3	2250	1550
done	5000	1459

prune399.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes669.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	24
1	26	24
done	26	24

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2652×	body	1280	valid
660.0ms	2568×	body	640	valid
464.0ms	8463×	body	80	valid
246.0ms	1426×	body	320	valid
90.0ms	762×	body	160	valid