Details

sample68.0ms

Algorithm

intervals

Results

40.0ms	253×	body	80	valid
7.0ms	10×	body	640	valid
2.0ms	5×	body	320	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5052
5	3741
4	818
3	257
2	102
1	51
0	21

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.1b	(pow (- (/ (+ m n) 2) M) 2)
32.6b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite903.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `add-cbrt-cube` `diff-log`
4×	`associate-r` `insert-posit16`
3×	`pow-unpow` `sub-neg` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `neg-log` `associate-*r/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

765.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
28.0ms	(* K (+ m n))
62.0ms	(pow (- (/ (+ m n) 2) M) 2)
45.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series433.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms	(* K (+ m n))
90.0ms	(pow (- (/ (+ m n) 2) M) 2)
81.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1280
1	451
0	175

prune850.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.1b	(pow (- (/ (+ m n) 2) M) 2)

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
27×	`add-log-exp`
18×	`add-sqr-sqrt`
14×	`distribute-lft-out--`
13×	`diff-log`
8×	`exp-prod`
7×	`add-cube-cbrt`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `difference-of-squares` `rem-exp-log`
4×	`sub-neg` `distribute-rgt-neg-in` `add-cbrt-cube` `neg-log` `insert-posit16`
3×	`pow-unpow` `exp-sum`
2×	`flip3--` `flip--` `associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `exp-diff` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

9.0ms	(- l (fabs (- m n)))
1.4s	(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
789.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms	(pow (- (/ (+ m n) 2) M) 2)

series449.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- l (fabs (- m n)))
136.0ms	(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
196.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
99.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify2.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5016
3	4031
2	1035
1	399
0	154

prune682.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

localize60.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (* K (+ m n)))
13.8b	(cbrt (* K (+ m n)))
13.8b	(cbrt (* K (+ m n)))
32.4b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 47

Calls

4 calls:

5.0ms	(cbrt (* K (+ m n)))
9.0ms	(cbrt (* K (+ m n)))
11.0ms	(cbrt (* K (+ m n)))
62.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

series559.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (* K (+ m n)))
144.0ms	(cbrt (* K (+ m n)))
157.0ms	(cbrt (* K (+ m n)))
78.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify1.4s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
4	2035
3	689
2	351
1	187
0	88

prune711.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

localize90.0ms

Local error

Found 4 expressions with local error:

12.6b	(cbrt (* n K))
13.8b	(cbrt (* K (+ m n)))
13.8b	(cbrt (* K (+ m n)))
28.4b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* n K))) 2) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `cbrt-div` `-un-lft-identity` `add-cbrt-cube` `associate-r/` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
2×	`cos-sum` `flip3-+` `flip-+`
1×	`cos-diff` `sub-neg`

Counts

4 → 45

Calls

4 calls:

3.0ms	(cbrt (* n K))
5.0ms	(cbrt (* K (+ m n)))
5.0ms	(cbrt (* K (+ m n)))
40.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* n K))) 2) M))

series631.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (* n K))
158.0ms	(cbrt (* K (+ m n)))
162.0ms	(cbrt (* K (+ m n)))
216.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* n K))) 2) M))

simplify2.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5007
4	3637
3	1156
2	513
1	259
0	120

prune674.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.2b

regimes944.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.9s	8100×	body	80	valid
223.0ms	134×	body	1280	valid
210.0ms	186×	body	640	valid
108.0ms	107×	body	320	valid
32.0ms	67×	body	160	valid
4.0ms	2×	body	2560	valid