Details

sample128.0ms

Algorithm

intervals

Results

71.0ms	259×	body	80	valid
4.0ms	3×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1428
4	534
3	208
2	93
1	50
0	21

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize80.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) K)
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))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
80×	`prod-diff`
63×	`exp-sum`
48×	`add-cube-cbrt`
37×	`unpow-prod-down`
25×	`difference-of-squares`
23×	`cos-sum`
19×	`distribute-lft-out--`
15×	`times-frac`
11×	`associate--l+`
10×	`add-log-exp`
8×	`exp-prod`
7×	`pow1` `add-exp-log` `sqr-pow`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`pow-unpow` `sub-neg` `diff-log` `associate-r` `div-inv` `rem-exp-log`
2×	`associate-*l/`
1×	`cos-diff` `pow-to-exp` `pow-pow` `flip3-+` `exp-diff` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

15.0ms	(* (+ m n) K)
89.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
926.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
58.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series654.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (+ m n) K)
325.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
191.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))
96.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2142
1	996
0	497

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize45.0ms

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)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

166×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
118×	`prod-diff`
68×	`unpow-prod-down`
63×	`exp-sum`
59×	`add-cube-cbrt`
49×	`difference-of-squares`
38×	`distribute-lft-out--`
22×	`associate--l+`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`times-frac`
8×	`exp-prod`
6×	`diff-log`
5×	`fma-neg`
4×	`pow1` `sub-neg` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `rem-exp-log`
1×	`associate--l-` `pow-to-exp` `pow-pow` `flip3--` `exp-diff` `pow-exp` `flip--`

Counts

3 → 193

Calls

3 calls:

281.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
65.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
807.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))

series852.0ms

Counts

3 → 9

Calls

3 calls:

261.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
401.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
189.0ms	(exp (- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0)))

simplify2.0s

Counts

202 → 202

Iterations

Iter	Nodes
done	5005
2	1706
1	694
0	318

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

183×	`sqrt-prod`
162×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
106×	`unpow-prod-up`
104×	`prod-diff`
74×	`unpow-prod-down`
63×	`add-cube-cbrt`
43×	`difference-of-squares`
29×	`distribute-lft-out--`
17×	`pow-unpow`
16×	`sqr-pow`
11×	`times-frac`
8×	`pow-pow`
6×	`pow1` `rem-sqrt-square` `exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`sub-neg` `exp-sum` `pow-sub`

Counts

4 → 214

Calls

4 calls:

59.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.2s	(pow (exp (+ (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))))
82.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
114.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

429.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
570.0ms	(pow (exp (+ (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))))
392.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
372.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify3.9s

Counts

226 → 226

Iterations

Iter	Nodes
done	5011
2	3262
1	1232
0	417

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize166.0ms

Local error

Found 4 expressions with local error:

35.8b	(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))
35.8b	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `sqrt-prod`
28×	`unpow-prod-down`
20×	`*-un-lft-identity`
12×	`rem-sqrt-square` `add-cube-cbrt`
8×	`difference-of-squares` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `sqrt-pow1` `times-frac` `add-cbrt-cube` `pow1/2` `add-exp-log` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`

Counts

4 → 96

Calls

4 calls:

96.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
114.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
99.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
125.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

424.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
395.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
393.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))
408.0ms	(sqrt (pow (- (/ (+ m n) 2.0) M) 2.0))

simplify2.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
5	2475
4	961
3	460
2	248
1	142
0	81

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

regimes708.0ms

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	20
1	20
0	16

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.9s	8076×	body	80	valid
136.0ms	118×	body	1280	valid
88.0ms	141×	body	640	valid
87.0ms	112×	body	320	valid
25.0ms	62×	body	160	valid
2.0ms	2×	body	2560	valid