Details

sample242.0ms

Algorithm

intervals

Results

87.0ms	87×	body	1280	valid
53.0ms	92×	body	640	valid
29.0ms	233×	body	80	valid
22.0ms	52×	body	320	valid
9.0ms	33×	body	160	valid

simplify5.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3492
6	1111
5	427
4	202
3	85
2	44
1	24
0	14

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.8b	(- (exp l) (exp (- l)))

rewrite285.0ms

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-exp-log` `add-cbrt-cube`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `flip--` `log1p-expm1-u`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 96

Calls

3 calls:

111.0ms	(* J (- (exp l) (exp (- l))))
133.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
30.0ms	(- (exp l) (exp (- l)))

series366.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(* J (- (exp l) (exp (- l))))
183.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
71.0ms	(- (exp l) (exp (- l)))

simplify6.1s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4419
2	1015
1	390
0	168

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
0.2b	(* (* l l) 1/3)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
14×	`pow1`
13×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp`
7×	`cbrt-unprod`
6×	`pow-prod-down`
5×	`associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp` `fma-udef`

Counts

4 → 78

Calls

4 calls:

1.0ms	(fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))
32.0ms	(* 1/60 (pow l 5))
39.0ms	(* (* J (fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
38.0ms	(* (* l l) 1/3)

series686.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))
92.0ms	(* 1/60 (pow l 5))
429.0ms	(* (* J (fma l (+ 2 (* (* l l) 1/3)) (* 1/60 (pow l 5)))) (cos (/ K 2.0)))
59.0ms	(* (* l l) 1/3)

simplify3.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1109
1	372
0	155

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
7×	`prod-exp` `fma-udef`
5×	`distribute-rgt-in` `distribute-lft-in` `cbrt-unprod`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 83

Calls

4 calls:

1.0ms	(fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5)))
25.0ms	(* 1/60 (pow l 5))
34.0ms	(* J (* (cos (/ K 2.0)) (fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5)))))
18.0ms	(* (cos (/ K 2.0)) (fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5))))

series1.1s

Counts

4 → 12

Calls

4 calls:

137.0ms	(fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5)))
96.0ms	(* 1/60 (pow l 5))
476.0ms	(* J (* (cos (/ K 2.0)) (fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5)))))
364.0ms	(* (cos (/ K 2.0)) (fma (fma 1/3 (* l l) 2) l (* 1/60 (pow l 5))))

simplify2.9s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1147
1	379
0	160

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* (* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0))) J)
0.1b	(* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0)))
2.5b	(* (* (* 1/60 (pow l 5)) (cos (/ K 2.0))) J)

rewrite365.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
29×	`add-cbrt-cube`
24×	`prod-exp`
23×	`pow1`
16×	`associate-r` `cbrt-unprod`
15×	`add-sqr-sqrt`
12×	`pow-prod-down`
10×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

24.0ms	(* 1/60 (pow l 5))
119.0ms	(* (* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0))) J)
45.0ms	(* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0)))
171.0ms	(* (* (* 1/60 (pow l 5)) (cos (/ K 2.0))) J)

series1.1s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* 1/60 (pow l 5))
667.0ms	(* (* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0))) J)
145.0ms	(* (* (fma 1/3 (* l l) 2) l) (cos (/ K 2.0)))
177.0ms	(* (* (* 1/60 (pow l 5)) (cos (/ K 2.0))) J)

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5004
2	1533
1	462
0	178

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes1.1s

Accuracy

57.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.4b

bsearch177.0ms

Steps

Iters	Range		Point
8	0.0008799215500326209	0.6307682633451466	0.016140146370427967

simplify21.0ms

Iterations

Iter	Nodes
done	58
1	58
0	41

end1.0ms

sample10.2s

Algorithm

intervals

Results

3.3s	2707×	body	1280	valid
2.7s	2588×	body	640	valid
2.1s	8329×	body	80	valid
808.0ms	1438×	body	320	valid
305.0ms	750×	body	160	valid