Details

sample94.0ms

Algorithm

intervals

Results

44.0ms	259×	body	80	valid
3.0ms	3×	body	1280	valid
3.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (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)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite10.2s

Algorithm

rewrite-expression-head

Rules

325×	`add-sqr-sqrt`
268×	`*-un-lft-identity`
261×	`prod-diff`
246×	`exp-sum`
126×	`unpow-prod-down` `associate-r`
120×	`add-cube-cbrt`
102×	`distribute-rgt-neg-in`
100×	`distribute-lft-neg-in`
91×	`difference-of-squares`
75×	`distribute-lft-out--`
30×	`times-frac`
23×	`cos-sum`
21×	`sqr-pow`
15×	`add-log-exp`
10×	`neg-mul-1`
8×	`exp-prod`
7×	`pow1`
6×	`add-cbrt-cube` `diff-log` `add-exp-log`
5×	`rem-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `sub-neg` `associate-l` `div-inv`
2×	`exp-diff` `neg-log` `associate--r-`
1×	`cos-diff` `pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 345

Calls

4 calls:

7.8s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.3s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
51.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
47.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.3s

Counts

4 → 12

Calls

4 calls:

575.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
193.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
409.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
105.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.1s

Counts

357 → 357

Iterations

Iter	Nodes
done	5000
2	3497
1	1179
0	608

prune3.5s

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

rewrite3.9s

Algorithm

rewrite-expression-head

Rules

330×	`add-sqr-sqrt`
277×	`*-un-lft-identity`
249×	`prod-diff`
138×	`unpow-prod-down`
123×	`exp-sum`
115×	`add-cube-cbrt`
114×	`distribute-rgt-neg-in`
110×	`distribute-lft-neg-in`
96×	`difference-of-squares`
83×	`distribute-lft-out--`
24×	`fma-neg` `add-log-exp`
23×	`times-frac` `sqr-pow`
12×	`diff-log`
11×	`neg-mul-1` `associate--r+`
8×	`exp-prod`
5×	`rem-exp-log`
4×	`pow1` `neg-log` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `flip3--` `exp-diff` `pow-exp` `flip--`

Counts

3 → 347

Calls

3 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.3s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
78.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series889.0ms

Counts

3 → 9

Calls

3 calls:

286.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
206.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
397.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.6s

Counts

356 → 356

Iterations

Iter	Nodes
done	5000
2	2752
1	831
0	394

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize117.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ m n) (sqrt 2.0))
0.5b	(/ (+ m n) (sqrt 2.0))
32.2b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
32.6b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`sqrt-prod`
14×	`distribute-lft-out`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 120

Calls

4 calls:

38.0ms	(/ (+ m n) (sqrt 2.0))
31.0ms	(/ (+ m n) (sqrt 2.0))
4.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
4.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ m n) (sqrt 2.0))
125.0ms	(/ (+ m n) (sqrt 2.0))
297.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
307.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify2.3s

Counts

132 → 132

Iterations

Iter	Nodes
done	5002
3	4146
2	782
1	250
0	134

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize187.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ m n) (sqrt 2.0))
0.6b	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))))
32.2b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
32.6b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`sqrt-prod`
7×	`distribute-lft-out`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`log-prod` `exp-prod` `fma-udef`
2×	`cos-sum` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `exp-diff` `sin-sum` `div-exp` `rem-log-exp` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

38.0ms	(/ (+ m n) (sqrt 2.0))
8.0ms	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))))
4.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
4.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (+ m n) (sqrt 2.0))
332.0ms	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))))
319.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
338.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	3772
2	823
1	289
0	161

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes844.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8067×	body	80	valid
114.0ms	137×	body	640	valid
88.0ms	99×	body	1280	valid
81.0ms	117×	body	320	valid
22.0ms	70×	body	160	valid
4.0ms	2×	body	2560	valid