Details

sample92.0ms

Algorithm

intervals

Results

38.0ms	260×	body	80	valid
17.0ms	4×	body	320	valid
7.0ms	7×	body	1280	valid
2.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (121.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	220	29
4	680	28
5	3210	28
done	5001	28

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

42×	`prod-diff`
40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
33×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`fma-neg` `div-inv`
6×	`unpow-prod-down`
5×	`add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 99

Calls

3 calls:

22.0ms	(- (/ (* K (+ m n)) 2.0) M)
80.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
77.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series631.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(- (/ (* K (+ m n)) 2.0) M)
438.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
86.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify775.0ms

Counts

108 → 108

Iterations

Useful iterations: done (767.0ms)

Iter	Nodes	Cost
0	268	2992
1	554	2393
2	1334	2015
done	5001	1843

prune518.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

120.0ms

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

series373.0ms

Counts

1 → 3

Calls

1 calls:

373.0ms

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

simplify896.0ms

Counts

25 → 25

Iterations

Useful iterations: done (894.0ms)

Iter	Nodes	Cost
0	76	357
1	194	338
2	455	325
3	1214	324
done	5000	316

prune131.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
0.4b	(/ K (sqrt 2.0))
0.4b	(/ (+ m n) (sqrt 2.0))
37.1b	(cos (+ (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M) (+ (- M) M)))

rewrite466.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
94×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
64×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`cos-diff` `associate-+l-` `frac-2neg` `clear-num` `associate-/l/`
1×	`neg-sub0` `frac-times` `associate-+r-` `cos-sum` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 184

Calls

4 calls:

68.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
13.0ms	(/ K (sqrt 2.0))
39.0ms	(/ (+ m n) (sqrt 2.0))
338.0ms	(cos (+ (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M) (+ (- M) M)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
72.0ms	(/ K (sqrt 2.0))
120.0ms	(/ (+ m n) (sqrt 2.0))
373.0ms	(cos (+ (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M) (+ (- M) M)))

simplify1.6s

Counts

196 → 196

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	231	2728
1	610	2451
2	3472	2269
done	5000	2264

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0))))
37.0b	(cos (+ (- (* (/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0)))) (* (/ K (sqrt (cbrt 2.0))) (/ (+ m n) (sqrt 2.0)))) M) (+ (- M) M)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`pow1`
12×	`times-frac`
11×	`pow-flip`
9×	`sqrt-pow1`
8×	`add-exp-log` `pow1/3`
6×	`cbrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`cos-diff` `associate-+l-` `div-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`cbrt-undiv` `pow2` `neg-sub0` `associate-+r-` `rec-exp` `cos-sum` `frac-2neg` `pow-plus` `pow1/2` `1-exp` `clear-num` `div-inv` `inv-pow`

Counts

4 → 85

Calls

4 calls:

2.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)
29.0ms	(/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0))))
1.5s	(cos (+ (- (* (/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0)))) (* (/ K (sqrt (cbrt 2.0))) (/ (+ m n) (sqrt 2.0)))) M) (+ (- M) M)))

series744.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0))))
744.0ms	(cos (+ (- (* (/ 1 (sqrt (* (cbrt 2.0) (cbrt 2.0)))) (* (/ K (sqrt (cbrt 2.0))) (/ (+ m n) (sqrt 2.0)))) M) (+ (- M) M)))

simplify2.7s

Counts

91 → 91

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	144	1252
1	255	887
2	642	737
3	2927	721
done	5000	719

prune741.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.8b

regimes327.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	20	19
done	20	19

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	8071×	body	80	valid
534.0ms	177×	body	640	valid
153.0ms	120×	body	1280	valid
46.0ms	103×	body	320	valid
17.0ms	54×	body	160	valid
3.0ms	2×	body	2560	valid