Details

sample65.0ms

Algorithm

intervals

Results

28.0ms	266×	body	80	valid
2.0ms	3×	body	1280	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3032
4	640
3	210
2	93
1	50
0	21

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

15.0ms	(- (/ (* K (+ m n)) 2.0) M)
28.0ms	(* K (+ m n))
99.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
29.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series602.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (/ (* K (+ m n)) 2.0) M)
49.0ms	(* K (+ m n))
362.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
90.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify783.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1216
1	421
0	164

prune805.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `pow-unpow` `add-exp-log` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `add-cbrt-cube` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `flip3--` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

1.2s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
87.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series709.0ms

Counts

2 → 6

Calls

2 calls:

278.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
431.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.5s

Counts

50 → 50

Iterations

Iter	Nodes
done	5004
3	3341
2	825
1	309
0	122

prune352.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.7b	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
36.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
12×	`unpow-prod-down`
11×	`log-pow` `add-cube-cbrt`
10×	`exp-prod`
8×	`pow1`
7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`associate-r` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `log-prod` `associate-l`
2×	`cos-sum` `times-frac` `associate-*r/` `distribute-lft-out--` `sqr-pow`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

31.0ms	(* K (+ m n))
74.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
302.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
32.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series892.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* K (+ m n))
390.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
363.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
89.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	4893
2	1103
1	407
0	174

prune806.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3)
0.7b	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
36.8b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`cbrt-prod` `unpow-prod-down`
11×	`log-pow`
10×	`exp-prod`
6×	`pow1` `cube-prod`
5×	`add-cbrt-cube` `add-exp-log`
4×	`add-log-exp`
3×	`pow-unpow` `log-prod` `sqr-pow`
2×	`cube-mult` `cos-sum` `unpow3` `difference-of-squares`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `times-frac` `pow1/3` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

5.0ms	(cbrt (pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3))
8.0ms	(pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3)
253.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
42.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series825.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3))
226.0ms	(pow (cos (- (/ (* (+ m n) K) 2.0) M)) 3)
402.0ms	(log (exp (pow (- (/ (+ m n) 2.0) M) 2.0)))
101.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
2	1232
1	331
0	160

prune920.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.8b

regimes628.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.1s	8120×	body	80	valid
106.0ms	153×	body	640	valid
96.0ms	107×	body	1280	valid
43.0ms	89×	body	320	valid
19.0ms	60×	body	160	valid
8.0ms	6×	body	2560	valid