Details

sample49.0ms

Algorithm

intervals

Results

22.0ms	254×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	7×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (85.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize22.0ms

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))
38.0b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite6.0s

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:

5.8s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
18.0ms	(* K (+ m n))
38.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series752.0ms

Counts

4 → 12

Calls

4 calls:

392.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(* K (+ m n))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

236 → 236

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	629	9112
1	1187	7956
2	2478	7237
done	5002	6804

prune686.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite57.0ms

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:

57.0ms

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

series274.0ms

Counts

1 → 3

Calls

1 calls:

274.0ms

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

simplify1.4s

Counts

25 → 25

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	76	357
1	160	338
2	323	325
3	767	324
4	1915	316
done	5000	315

prune121.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt K)
0.5b	(cbrt K)
0.5b	(cbrt K)
37.9b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite94.0ms

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)
87.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series643.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt K)
180.0ms	(cbrt K)
179.0ms	(cbrt K)
106.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.4s

Counts

84 → 84

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	202	2442
1	342	2034
2	633	1482
3	1901	1089
done	5000	987

prune362.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
37.6b	(cos (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (cbrt 2.0) (cbrt 2.0))) M))
38.1b	(sin (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (cbrt 2.0) (cbrt 2.0))) M))

rewrite733.0ms

Algorithm

rewrite-expression-head

Rules

1542×	`times-frac`
882×	`*-un-lft-identity`
666×	`add-sqr-sqrt` `add-cube-cbrt`
594×	`prod-diff`
299×	`cos-sum` `sin-sum`
222×	`cbrt-prod`
108×	`distribute-lft-out`
42×	`associate-/r/`
30×	`div-inv`
18×	`flip3-+` `flip-+`
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 → 644

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
317.0ms	(cos (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (cbrt 2.0) (cbrt 2.0))) M))
318.0ms	(sin (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (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)
198.0ms	(cos (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (cbrt 2.0) (cbrt 2.0))) M))
415.0ms	(sin (- (/ (/ K (/ (cbrt 2.0) (+ m n))) (* (cbrt 2.0) (cbrt 2.0))) M))

simplify1.7s

Counts

652 → 652

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	2111	59384
1	3482	46788
done	5000	41702

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.2b

regimes515.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample1.2s

Algorithm

intervals

Results

636.0ms	8107×	body	80	valid
60.0ms	121×	body	1280	valid
51.0ms	145×	body	640	valid
25.0ms	104×	body	320	valid
9.0ms	55×	body	160	valid
2.0ms	3×	body	2560	valid