Details

sample85.0ms

Algorithm

intervals

Results

45.0ms	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

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (259.0ms)

Iter	Nodes	Cost
0	21	826
1	50	826
2	95	826
3	220	826
4	684	786
5	3247	786
done	5000	786

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize85.0ms

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))

rewrite10.0s

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:

7.7s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.2s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

551.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
178.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
360.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
101.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.8s

Counts

357 → 357

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	608	370443
1	1179	339589
2	3497	313612
done	5000	313538

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize28.0ms

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)

rewrite3.8s

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:

1.4s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.2s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
96.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series824.0ms

Counts

3 → 9

Calls

3 calls:

259.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
171.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
394.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.8s

Counts

356 → 356

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	394	346751
1	831	315027
2	2752	283095
done	5000	283021

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize92.0ms

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))))

rewrite53.0ms

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:

30.0ms	(/ (+ m n) (sqrt 2.0))
16.0ms	(/ (+ m n) (sqrt 2.0))
2.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

series854.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (+ m n) (sqrt 2.0))
119.0ms	(/ (+ m n) (sqrt 2.0))
292.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
315.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify2.3s

Counts

132 → 132

Iterations

Useful iterations: 3 (859.0ms)

Iter	Nodes	Cost
0	134	40129
1	250	36852
2	782	36522
3	4146	34417
done	5002	34417

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize128.0ms

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))))

rewrite49.0ms

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:

30.0ms	(/ (+ m n) (sqrt 2.0))
7.0ms	(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:

143.0ms	(/ (+ m n) (sqrt 2.0))
330.0ms	(log (exp (cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))))
332.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
268.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify2.6s

Counts

100 → 100

Iterations

Useful iterations: 3 (967.0ms)

Iter	Nodes	Cost
0	161	37398
1	289	32012
2	823	31397
3	3772	27572
done	5000	27652

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes697.0ms

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: 1 (3.0ms)

Iter	Nodes	Cost
0	17	646
1	21	605
2	22	605
done	22	605

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	8067×	body	80	valid
507.0ms	137×	body	640	valid
122.0ms	99×	body	1280	valid
104.0ms	117×	body	320	valid
21.0ms	70×	body	160	valid
3.0ms	2×	body	2560	valid