Details

sample249.0ms

Algorithm

intervals

Results

97.0ms	76×	body	1280	valid
45.0ms	81×	body	640	valid
34.0ms	277×	body	80	valid
19.0ms	50×	body	320	valid
6.0ms	27×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	45	14
3	91	14
4	222	14
5	600	14
6	2862	14
done	5000	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
5.7b	(- (exp l) (exp (- l)))

rewrite101.0ms

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:

62.0ms	(* J (- (exp l) (exp (- l))))
0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
34.0ms	(- (exp l) (exp (- l)))

series370.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* J (- (exp l) (exp (- l))))
233.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
55.0ms	(- (exp l) (exp (- l)))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	162	1865
1	370	1449
2	1562	1126
done	5000	954

prune421.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.1b	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

rewrite20.0ms

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:

1.0ms	(fma 1/60 (pow l 5) (* 2 l))
15.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
1.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
1.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

series909.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(fma 1/60 (pow l 5) (* 2 l))
179.0ms	(* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))))
106.0ms	(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
404.0ms	(fma (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)

simplify896.0ms

Counts

64 → 64

Iterations

Useful iterations: done (893.0ms)

Iter	Nodes	Cost
0	97	1182
1	208	1165
2	824	1014
done	5000	998

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.1b	(fma (+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
0.3b	(* 1/3 J)
3.9b	(* (* 1/3 J) (pow l 3))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

38.0ms	(+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l))))
0.0ms	(fma (+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
9.0ms	(* 1/3 J)
40.0ms	(* (* 1/3 J) (pow l 3))

series656.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l))))
342.0ms	(fma (+ (* (* 1/3 J) (pow l 3)) (* J (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)) U)
26.0ms	(* 1/3 J)
71.0ms	(* (* 1/3 J) (pow l 3))

simplify2.0s

Counts

89 → 89

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	145	1273
1	386	1155
2	2079	1041
done	5000	1038

prune634.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt J) (cbrt J))
0.6b	(cbrt J)
0.6b	(cbrt J)
0.6b	(cbrt J)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `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 → 81

Calls

4 calls:

24.0ms	(* (cbrt J) (cbrt J))
2.0ms	(cbrt J)
2.0ms	(cbrt J)
2.0ms	(cbrt J)

series1.6s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (cbrt J) (cbrt J))
352.0ms	(cbrt J)
680.0ms	(cbrt J)
283.0ms	(cbrt J)

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	65	554
1	143	443
2	719	423
done	5000	409

prune654.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes468.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.9s

Algorithm

intervals

Results

2.3s	2740×	body	1280	valid
2.0s	2561×	body	640	valid
1.7s	8516×	body	80	valid
694.0ms	1524×	body	320	valid
162.0ms	741×	body	160	valid