Details

sample61.0ms

Algorithm

intervals

Results

27.0ms	253×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (150.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	220	29
4	680	28
5	3210	28
done	5001	28

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

193×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
72×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
49×	`difference-of-squares`
42×	`distribute-lft-out--`
24×	`times-frac` `fma-neg`
23×	`cos-sum`
14×	`add-log-exp`
12×	`sqr-pow`
11×	`add-exp-log` `add-cbrt-cube` `associate--r+`
6×	`pow1` `neg-mul-1` `diff-log`
4×	`expm1-log1p-u` `associate-r/` `associate-r*` `log1p-expm1-u` `div-inv`
3×	`sub-neg` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `neg-log` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `flip--` `distribute-lft-out` `associate-/l` `associate--r-` `unswap-sqr`

Counts

4 → 262

Calls

4 calls:

26.0ms	(/ (* K (+ m n)) 2.0)
2.0s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
44.0ms	(* K (+ m n))
62.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series427.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (* K (+ m n)) 2.0)
258.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
35.0ms	(* K (+ m n))
79.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.8s

Counts

274 → 274

Iterations

Useful iterations: 2 (690.0ms)

Iter	Nodes	Cost
0	474	11220
1	1033	8873
2	3510	7208
done	5000	7208

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

94.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
2.0s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series577.0ms

Counts

2 → 6

Calls

2 calls:

337.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
240.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify2.3s

Counts

207 → 207

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	274	9396
1	649	7425
2	2048	6187
done	5000	5080

prune660.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
44×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
9×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 112

Calls

4 calls:

4.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series474.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
99.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
80.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
78.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.6s

Counts

124 → 124

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	190	5299
1	323	4146
2	596	3412
3	1577	2959
done	5001	2653

prune749.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

92×	`cos-sum`
84×	`prod-diff`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
23×	`log-div` `exp-diff`
12×	`div-inv`
5×	`pow1`
4×	`add-exp-log` `cos-diff` `expm1-log1p-u` `sub-neg` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 140

Calls

4 calls:

114.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series377.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
93.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
83.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.9s

Counts

152 → 152

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	292	6984
1	515	5325
2	1093	4370
3	2554	3770
done	5000	3362

prune827.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

regimes493.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
2	22	18
done	22	18

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	8095×	body	80	valid
473.0ms	101×	body	1280	valid
90.0ms	149×	body	640	valid
40.0ms	90×	body	320	valid
16.0ms	55×	body	160	valid
2.0ms	2×	body	2560	valid