Details

sample97.0ms

Algorithm

intervals

Results

49.0ms	262×	body	80	valid
3.0ms	3×	body	1280	valid
2.0ms	3×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	2×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3247
4	684
3	220
2	95
1	50
0	21

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* (+ m n) (/ K 2.0))
33.3b	(cos (- (* (+ m n) (/ K 2.0)) M))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
60×	`times-frac`
51×	`prod-diff`
16×	`fma-neg`
13×	`associate-r` `distribute-lft-out`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down` `add-log-exp`
5×	`cos-sum` `div-inv`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow`
2×	`frac-times` `sub-neg` `flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`
1×	`cos-diff` `pow-to-exp` `cbrt-undiv` `pow-pow` `flip3--` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `flip--` `sqr-pow`

Counts

4 → 157

Calls

4 calls:

65.0ms	(- (/ (+ m n) 2.0) M)
76.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(* (+ m n) (/ K 2.0))
42.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series602.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ (+ m n) 2.0) M)
419.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
49.0ms	(* (+ m n) (/ K 2.0))
95.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify1.7s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	3020
1	740
0	300

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ (+ m n) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
50×	`times-frac`
48×	`prod-diff`
16×	`fma-neg`
12×	`distribute-lft-out`
6×	`unpow-prod-down`
4×	`div-inv` `add-log-exp` `difference-of-squares`
3×	`pow1` `pow-unpow` `add-exp-log`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 103

Calls

2 calls:

60.0ms	(- (/ (+ m n) 2.0) M)
97.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series402.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (/ (+ m n) 2.0) M)
360.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify741.0ms

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1174
1	422
0	172

prune647.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0)))
0.4b	(/ (+ n m) (sqrt 2.0))
0.5b	(/ K (sqrt 2.0))
33.4b	(cos (- (* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0))) M))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
65×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-l`
22×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`prod-diff`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 187

Calls

4 calls:

54.0ms	(* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0)))
36.0ms	(/ (+ n m) (sqrt 2.0))
9.0ms	(/ K (sqrt 2.0))
53.0ms	(cos (- (* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0))) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

304.0ms	(* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0)))
105.0ms	(/ (+ n m) (sqrt 2.0))
82.0ms	(/ K (sqrt 2.0))
638.0ms	(cos (- (* (/ (+ n m) (sqrt 2.0)) (/ K (sqrt 2.0))) M))

simplify1.4s

Counts

199 → 199

Iterations

Iter	Nodes
done	5000
2	3389
1	665
0	264

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ (+ m n) (sqrt 2.0)))
0.6b	(cbrt (/ (+ m n) (sqrt 2.0)))
0.6b	(cbrt (/ (+ m n) (sqrt 2.0)))
33.4b	(cos (- (* (* (* (cbrt (/ (+ m n) (sqrt 2.0))) (cbrt (/ (+ m n) (sqrt 2.0)))) (cbrt (/ (+ m n) (sqrt 2.0)))) (/ K (sqrt 2.0))) M))

rewrite826.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
84×	`cbrt-prod`
72×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`sqrt-prod`
18×	`distribute-lft-out`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `prod-diff` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 132

Calls

4 calls:

11.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
11.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
7.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
786.0ms	(cos (- (* (* (* (cbrt (/ (+ m n) (sqrt 2.0))) (cbrt (/ (+ m n) (sqrt 2.0)))) (cbrt (/ (+ m n) (sqrt 2.0)))) (/ K (sqrt 2.0))) M))

series2.7s

Counts

4 → 12

Calls

4 calls:

691.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
593.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
643.0ms	(cbrt (/ (+ m n) (sqrt 2.0)))
727.0ms	(cos (- (* (* (* (cbrt (/ (+ m n) (sqrt 2.0))) (cbrt (/ (+ m n) (sqrt 2.0)))) (cbrt (/ (+ m n) (sqrt 2.0)))) (/ K (sqrt 2.0))) M))

simplify1.8s

Counts

144 → 144

Iterations

Iter	Nodes
done	5001
3	3129
2	872
1	348
0	198

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes561.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.0s	8127×	body	80	valid
177.0ms	119×	body	1280	valid
160.0ms	167×	body	640	valid
48.0ms	104×	body	320	valid
15.0ms	47×	body	160	valid
6.0ms	4×	body	2560	valid