Details

sample96.0ms

Algorithm

intervals

Results

46.0ms	255×	body	80	valid
8.0ms	7×	body	1280	valid
6.0ms	9×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	2×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 4 (165.0ms)

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.0b

localize57.0ms

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	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite10.0s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
141×	`prod-diff`
130×	`associate-r`
123×	`exp-sum`
72×	`add-cube-cbrt`
66×	`unpow-prod-down`
50×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`difference-of-squares`
35×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
11×	`sqr-pow`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `div-inv`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-exp` `flip-+` `distribute-lft-out` `associate--r-`

Counts

4 → 224

Calls

4 calls:

9.8s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
89.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(* K (+ m n))
71.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

593.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
339.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(* K (+ m n))
113.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.4s

Counts

236 → 236

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	629	9112
1	1290	7977
2	4122	7389
done	5000	7385

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.9b

localize34.0ms

Local error

Found 1 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

91.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series390.0ms

Counts

1 → 3

Calls

1 calls:

390.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify954.0ms

Counts

25 → 25

Iterations

Useful iterations: done (953.0ms)

Iter	Nodes	Cost
0	76	357
1	194	338
2	455	325
3	1214	324
done	5000	316

prune173.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
35.2b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)
113.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

323.0ms	(cbrt K)
279.0ms	(cbrt K)
263.0ms	(cbrt K)
163.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify2.4s

Counts

84 → 84

Iterations

Useful iterations: 3 (843.0ms)

Iter	Nodes	Cost
0	202	2442
1	365	2048
2	884	1482
3	3946	1089
done	5000	1089

prune566.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.9b	(sin (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))
35.3b	(cos (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
84×	`prod-diff`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
44×	`cos-sum` `sin-sum`
24×	`cbrt-prod`
12×	`div-inv`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `pow1/3`
1×	`cos-diff` `sin-diff`

Counts

4 → 134

Calls

4 calls:

2.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)
148.0ms	(sin (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))
168.0ms	(cos (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))

series613.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
315.0ms	(sin (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))
298.0ms	(cos (- (/ (/ (* (+ m n) K) (cbrt 2.0)) (* (cbrt 2.0) (cbrt 2.0))) M))

simplify2.6s

Counts

142 → 142

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	437	8308
1	768	6764
2	1518	5474
3	4454	4330
done	5000	4330

prune955.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.8b

regimes586.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s	8039×	body	80	valid
102.0ms	159×	body	640	valid
100.0ms	111×	body	1280	valid
44.0ms	100×	body	320	valid
21.0ms	67×	body	160	valid
8.0ms	5×	body	2560	valid