Details

sample100.0ms

Algorithm

intervals

Results

50.0ms	260×	body	80	valid
2.0ms	3×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 4 (169.0ms)

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize32.0ms

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)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.3s

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:

27.0ms	(* K (+ m n))
636.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
117.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
487.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series718.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* K (+ m n))
220.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
366.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
86.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.1s

Counts

130 → 130

Iterations

Useful iterations: 3 (1.5s)

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

prune754.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

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)

rewrite690.0ms

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:

583.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
105.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series613.0ms

Counts

2 → 6

Calls

2 calls:

242.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
371.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.1s

Counts

66 → 66

Iterations

Useful iterations: done (3.1s)

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

prune368.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.5b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`cos-sum`
21×	`prod-diff`
12×	`cbrt-prod` `unpow-prod-down`
10×	`times-frac`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `difference-of-squares`
1×	`cos-diff` `sub-neg` `pow1/3` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 103

Calls

4 calls:

82.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
7.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
20.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series781.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
117.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
208.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
94.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.7s

Counts

115 → 115

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	284	3075
1	509	2459
2	935	2130
3	3359	1970
done	5001	1859

prune651.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite153.0ms

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:

4.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series501.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
97.0ms	(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

prune686.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes191.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8120×	body	80	valid
116.0ms	142×	body	1280	valid
110.0ms	140×	body	640	valid
41.0ms	95×	body	320	valid
18.0ms	61×	body	160	valid
4.0ms	4×	body	2560	valid