Details

sample53.0ms

Algorithm

intervals

Results

26.0ms	261×	body	80	valid
2.0ms	4×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	2×	body	320	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (196.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	197	29
4	465	28
5	1141	28
6	4709	28
done	5000	28

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(* (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))) (cos (- (/ (* K (+ m n)) 2.0) M)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

21.0ms	(* K (+ m n))
3.9s	(* (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))) (cos (- (/ (* K (+ m n)) 2.0) M)))
90.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.4s

Counts

4 → 12

Calls

4 calls:

36.0ms	(* K (+ m n))
498.0ms	(* (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))) (cos (- (/ (* K (+ m n)) 2.0) M)))
750.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
91.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.1s

Counts

90 → 90

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	211	1770
1	505	1714
2	1377	1536
3	4587	1533
done	5001	1532

prune564.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`add-cbrt-cube` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 34

Calls

2 calls:

13.0ms	(- (fabs (- m n)) l)
88.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series417.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (fabs (- m n)) l)
377.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.0s

Counts

40 → 40

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	104	508
1	216	486
2	424	461
3	947	457
4	2263	449
done	5000	448

prune210.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
32.2b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

14.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
17.0ms	(cbrt (* K (+ m n)))
95.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series545.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (* K (+ m n)))
138.0ms	(cbrt (* K (+ m n)))
166.0ms	(cbrt (* K (+ m n)))
83.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify2.9s

Counts

55 → 55

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	86	881
1	186	859
2	355	602
3	714	545
4	1391	521
5	3182	506
done	5001	500

prune441.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize55.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (* K (+ m n)))
14.9b	(cbrt (* K (+ m n)))
15.8b	(cbrt (* m K))
30.3b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

7.0ms	(cbrt (* K (+ m n)))
7.0ms	(cbrt (* K (+ m n)))
3.0ms	(cbrt (* m K))
59.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

series665.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(cbrt (* K (+ m n)))
170.0ms	(cbrt (* K (+ m n)))
81.0ms	(cbrt (* m K))
224.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* m K))) 2.0) M))

simplify2.2s

Counts

53 → 53

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	118	815
1	257	803
2	523	720
3	1106	693
4	2684	666
done	5000	663

prune438.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes361.0ms

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: 1 (2.0ms)

Iter	Nodes	Cost
0	16	19
1	20	17
done	20	17

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.6s	8086×	body	80	valid
122.0ms	106×	body	320	valid
116.0ms	142×	body	640	valid
99.0ms	124×	body	1280	valid
12.0ms	47×	body	160	valid
2.0ms	1×	body	2560	valid