Details

sample66.0ms

Algorithm

intervals

Results

28.0ms	259×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	4997
5	1382
4	501
3	198
2	91
1	50
0	21

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) (/ K 2.0))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
34.7b	(cos (- (* (+ m n) (/ K 2.0)) M))

rewrite926.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

25.0ms	(* (+ m n) (/ K 2.0))
56.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
798.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
44.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series738.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ m n) (/ K 2.0))
362.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
219.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
115.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1595
1	590
0	235

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`add-log-exp`
8×	`exp-prod` `unpow-prod-down` `difference-of-squares`
7×	`distribute-lft-out--`
6×	`diff-log` `add-cube-cbrt`
4×	`pow1` `sub-neg` `exp-sum` `associate--l+` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `sqr-pow` `rem-exp-log`
1×	`associate--l-` `pow-to-exp` `pow-pow` `times-frac` `flip3--` `exp-diff` `pow-exp` `flip--`

Counts

3 → 64

Calls

3 calls:

211.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
75.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
793.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))

series906.0ms

Counts

3 → 9

Calls

3 calls:

312.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
391.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
203.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))

simplify2.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
3	3373
2	930
1	380
0	152

prune697.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
11×	`pow-unpow` `unpow-prod-down`
8×	`add-log-exp` `difference-of-squares`
7×	`add-cube-cbrt` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`unpow-prod-up` `sub-neg` `associate--l+` `sqr-pow`
3×	`add-cbrt-cube` `diff-log` `pow-exp`
2×	`pow-to-exp` `pow-pow`
1×	`associate--l-` `e-exp-1` `times-frac` `flip3--` `flip--` `pow-sub`

Counts

3 → 69

Calls

3 calls:

194.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
172.0ms	(pow E (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
101.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series971.0ms

Counts

3 → 9

Calls

3 calls:

231.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
284.0ms	(pow E (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
455.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.8s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
3	3408
2	1091
1	439
0	169

prune710.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(pow (pow E (+ (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0)))) (- (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))))
35.8b	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
35.8b	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

rewrite473.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
34×	`sqrt-prod`
33×	`unpow-prod-down`
26×	`*-un-lft-identity`
17×	`pow-unpow`
14×	`difference-of-squares`
13×	`add-cube-cbrt`
9×	`sqr-pow`
7×	`pow-exp` `add-exp-log` `distribute-lft-out--`
6×	`rem-sqrt-square`
5×	`pow1`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-up` `times-frac`
2×	`pow-pow` `sqrt-pow1` `pow1/2`
1×	`e-exp-1` `sub-neg` `pow-sub`

Counts

4 → 103

Calls

4 calls:

73.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
188.0ms	(pow (pow E (+ (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0)))) (- (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))))
97.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
112.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series2.3s

Counts

4 → 12

Calls

4 calls:

377.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.1s	(pow (pow E (+ (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0)))) (- (sqrt (- (fabs (- m n)) l)) (sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))))
414.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
451.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify3.3s

Counts

115 → 115

Iterations

Iter	Nodes
done	5002
2	1550
1	614
0	231

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

regimes629.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8076×	body	80	valid
96.0ms	118×	body	1280	valid
83.0ms	141×	body	640	valid
56.0ms	62×	body	160	valid
48.0ms	112×	body	320	valid
2.0ms	2×	body	2560	valid