Details

sample92.0ms

Algorithm

intervals

Results

51.0ms	261×	body	80	valid
6.0ms	5×	body	1280	valid
3.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (138.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	207	29
4	499	28
5	1209	28
6	4807	28
done	5000	28

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

40.0ms	(* K (+ m n))
610.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
1.3s	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series641.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* K (+ m n))
290.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
195.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
107.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.4s

Counts

127 → 127

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	327	3025
1	661	2509
2	1550	2173
done	5000	2039

prune827.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize34.0ms

Local error

Found 3 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))))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `add-log-exp`
12×	`unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
5×	`exp-prod`
4×	`pow1` `add-exp-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `rem-exp-log`
2×	`associate-+r-` `times-frac` `diff-log` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `exp-diff` `exp-sum` `pow-exp` `flip-+`

Counts

3 → 79

Calls

3 calls:

117.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
519.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
1.5s	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

series829.0ms

Counts

3 → 9

Calls

3 calls:

369.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
263.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
196.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

simplify2.7s

Counts

88 → 88

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	175	1493
1	404	1359
2	1037	1250
3	4136	1231
done	5000	1229

prune503.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 3 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))))
0.0b	(pow E (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
8×	`pow-unpow` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `sqr-pow`
2×	`pow-to-exp` `associate-+r-` `pow-pow` `times-frac` `sum-log`
1×	`unpow-prod-up` `+-commutative` `sub-neg` `e-exp-1` `flip3-+` `diff-log` `flip-+` `pow-sub`

Counts

3 → 84

Calls

3 calls:

76.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
633.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
537.0ms	(pow E (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

series853.0ms

Counts

3 → 9

Calls

3 calls:

366.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
271.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
216.0ms	(pow E (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))

simplify3.4s

Counts

93 → 93

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	192	1743
1	458	1562
2	1160	1456
3	4551	1435
done	5000	1433

prune483.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ K (sqrt 2.0))
0.4b	(/ K (sqrt 2.0))
32.5b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
32.9b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 102

Calls

4 calls:

6.0ms	(/ K (sqrt 2.0))
10.0ms	(/ K (sqrt 2.0))
5.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
5.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series781.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ K (sqrt 2.0))
68.0ms	(/ K (sqrt 2.0))
312.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
325.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify3.0s

Counts

114 → 114

Iterations

Useful iterations: 3 (274.0ms)

Iter	Nodes	Cost
0	117	1264
1	185	1180
2	319	1104
3	547	984
4	1429	984
done	5000	984

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes317.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	22	20
done	22	20

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	8103×	body	80	valid
106.0ms	133×	body	1280	valid
86.0ms	161×	body	640	valid
71.0ms	113×	body	320	valid
13.0ms	53×	body	160	valid
3.0ms	3×	body	2560	valid