Details

sample46.0ms

Algorithm

intervals

Results

22.0ms	262×	body	80	valid
2.0ms	6×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	93	16
2	200	16
3	517	15
4	1893	15
5	5001	15
done	5001	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
31.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-log-exp`
9×	`add-cube-cbrt`
8×	`exp-prod`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `exp-sum` `difference-of-squares`
2×	`sub-neg` `cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `exp-diff` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

20.0ms	(* K (+ m n))
1.8s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
59.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series485.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* K (+ m n))
137.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
257.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify42.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	437	613
1	1474	567
2	5001	562
done	5001	562

prune340.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`diff-log`
8×	`exp-prod`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `exp-sum` `add-cbrt-cube`
2×	`associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `exp-diff` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 68

Calls

3 calls:

988.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.8s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
60.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series592.0ms

Counts

3 → 9

Calls

3 calls:

191.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
133.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify38.0ms

Counts

77 → 77

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	356	720
1	1112	675
2	5002	670
done	5002	670

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))) (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
36.5b	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
36.5b	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
36.5b	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

173×	`*-un-lft-identity`
100×	`cbrt-prod`
90×	`distribute-lft-out--`
37×	`add-sqr-sqrt`
31×	`swap-sqr`
30×	`distribute-rgt-neg-in`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1` `associate-r` `associate-l`
9×	`flip3--` `pow1/3` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 137

Calls

4 calls:

3.3s	(* (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))) (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
406.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
405.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
410.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

774.0ms	(* (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))) (cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
538.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
536.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
532.0ms	(cbrt (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify54.0ms

Counts

149 → 149

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	344	3344
1	1171	3195
2	5001	2715
done	5001	2715

prune473.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
31.8b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
275.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series510.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ m n))
130.0ms	(cbrt (+ m n))
140.0ms	(cbrt (+ m n))
108.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify154.0ms

Counts

64 → 64

Iterations

Useful iterations: 4 (149.0ms)

Iter	Nodes	Cost
0	186	485
1	416	445
2	1213	439
3	4532	439
4	5001	433
done	5001	433

prune333.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

regimes139.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	33
1	27	33
2	27	33
done	27	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

610.0ms	8136×	body	80	valid
57.0ms	124×	body	1280	valid
53.0ms	166×	body	640	valid
20.0ms	89×	body	320	valid
7.0ms	46×	body	160	valid
2.0ms	3×	body	2560	valid