Details

sample52.0ms

Algorithm

intervals

Results

26.0ms	255×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	4×	body	320	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (154.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	207	29
4	499	28
5	1209	28
6	4807	28
done	5000	28

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite891.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`prod-diff`
29×	`add-cube-cbrt`
23×	`cos-sum`
12×	`unpow-prod-down`
11×	`associate-+r+` `times-frac`
10×	`fma-def`
9×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `associate-l` `div-inv` `distribute-lft-out` `distribute-lft-out--`
2×	`sub-neg` `flip3-+` `associate-*r/` `sum-log` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

35.0ms	(* K (+ m n))
666.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
113.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
71.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series805.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* K (+ m n))
286.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
367.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
109.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.2s

Counts

130 → 130

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	348	2962
1	691	2434
2	1460	2132
3	4532	1966
done	5000	1966

prune795.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite708.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
12×	`add-cube-cbrt` `unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
7×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `pow-unpow` `distribute-lft-out--`
2×	`expm1-log1p-u` `times-frac` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

2 → 60

Calls

2 calls:

581.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
124.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series650.0ms

Counts

2 → 6

Calls

2 calls:

255.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
395.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.7s

Counts

66 → 66

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	144	1073
1	323	956
2	726	889
3	2545	876
done	5001	858

prune318.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
33.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
154.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt K)
287.0ms	(cbrt K)
293.0ms	(cbrt K)
151.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify2.3s

Counts

84 → 84

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	202	2442
1	342	2034
2	633	1482
3	1901	1089
done	5000	987

prune463.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
41.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
50.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series550.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
105.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
111.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
91.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify4.9s

Counts

124 → 124

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	190	5299
1	300	4088
2	413	3412
3	711	2959
4	1159	2527
5	1837	1537
6	3519	1510
done	5001	1470

prune584.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

regimes383.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.1s	8072×	body	80	valid
112.0ms	123×	body	1280	valid
104.0ms	167×	body	640	valid
47.0ms	100×	body	320	valid
13.0ms	42×	body	160	valid
9.0ms	6×	body	2560	valid