Details

sample62.0ms

Algorithm

intervals

Results

29.0ms	266×	body	80	valid
2.0ms	3×	body	1280	valid
2.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3247
4	684
3	220
2	95
1	50
0	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `prod-diff`
36×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`pow1` `fma-neg` `add-exp-log` `div-inv`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

34.0ms	(- (/ (* K (+ m n)) 2.0) M)
22.0ms	(* K (+ m n))
68.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
37.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series617.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (/ (* K (+ m n)) 2.0) M)
47.0ms	(* K (+ m n))
404.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
92.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify801.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1766
1	663
0	304

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.4s

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` `pow-unpow` `add-exp-log`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `neg-log` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `flip3--` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

1.3s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
62.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series673.0ms

Counts

2 → 6

Calls

2 calls:

285.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
387.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.0s

Counts

207 → 207

Iterations

Iter	Nodes
done	5000
2	2027
1	646
0	274

prune734.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.7b	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
36.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`cos-sum`
21×	`prod-diff`
12×	`unpow-prod-down`
11×	`times-frac` `log-pow`
10×	`exp-prod`
8×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `log-prod` `associate-l` `div-inv`
2×	`associate-*r/` `distribute-lft-out--` `sqr-pow`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

16.0ms	(* K (+ m n))
86.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
233.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
46.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series896.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* K (+ m n))
368.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
409.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
85.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify736.0ms

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
2	1577
1	641
0	315

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
37.0b	(cos (+ (- (* (/ K (cbrt 2.0)) (/ (/ (+ m n) (cbrt 2.0)) (cbrt 2.0))) M) (fma M -1 M)))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `cos-sum` `associate-+l-`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
341.0ms	(cos (+ (- (* (/ K (cbrt 2.0)) (/ (/ (+ m n) (cbrt 2.0)) (cbrt 2.0))) M) (fma M -1 M)))

series329.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
328.0ms	(cos (+ (- (* (/ K (cbrt 2.0)) (/ (/ (+ m n) (cbrt 2.0)) (cbrt 2.0))) M) (fma M -1 M)))

simplify3.1s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	2668
3	686
2	259
1	130
0	72

prune528.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

regimes636.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	8120×	body	80	valid
570.0ms	153×	body	640	valid
98.0ms	107×	body	1280	valid
39.0ms	89×	body	320	valid
21.0ms	60×	body	160	valid
8.0ms	6×	body	2560	valid