Details

sample118.0ms

Algorithm

intervals

Results

64.0ms	260×	body	80	valid
8.0ms	7×	body	1280	valid
2.0ms	3×	body	640	valid
2.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (107.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	210	29
4	640	28
5	3078	28
done	5000	28

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize51.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
6×	`unpow-prod-down`
5×	`add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `cos-sum` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 44

Calls

3 calls:

24.0ms	(- (/ (* K (+ m n)) 2.0) M)
125.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series559.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(- (/ (* K (+ m n)) 2.0) M)
400.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
80.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.7s

Counts

53 → 53

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	130	801
1	310	757
2	721	706
3	2086	699
done	5002	691

prune313.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 1 expressions with local error:

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

rewrite78.0ms

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×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

77.0ms

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

series369.0ms

Counts

1 → 3

Calls

1 calls:

369.0ms

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

simplify849.0ms

Counts

23 → 23

Iterations

Useful iterations: done (847.0ms)

Iter	Nodes	Cost
0	74	337
1	191	318
2	445	305
3	1197	304
done	5000	296

prune128.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.5b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
36.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

59.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
10.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
5.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
37.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series808.0ms

Counts

4 → 12

Calls

4 calls:

395.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
109.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
238.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.6s

Counts

86 → 86

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	143	1527
1	367	1327
2	1364	1175
done	5000	1174

prune501.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize56.0ms

Local error

Found 4 expressions with local error:

16.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
16.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
16.5b	(cbrt (- (/ (* K (+ m n)) 2.0) M))
46.0b	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 52

Calls

4 calls:

21.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
13.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
98.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

series1.2s

Counts

4 → 12

Calls

4 calls:

357.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
342.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
425.0ms	(cbrt (- (/ (* K (+ m n)) 2.0) M))
95.0ms	(cos (* (* (cbrt (- (/ (* K (+ m n)) 2.0) M)) (cbrt (- (/ (* K (+ m n)) 2.0) M))) (cbrt (- (/ (* K (+ m n)) 2.0) M))))

simplify1.0s

Counts

64 → 64

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	97	1446
1	215	1414
2	516	1119
3	1735	1020
done	5000	984

prune500.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

regimes251.0ms

Accuracy

0% (0.2b remaining)

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

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

sample3.0s

Algorithm

intervals

Results

2.0s	8071×	body	80	valid
152.0ms	177×	body	640	valid
107.0ms	120×	body	1280	valid
96.0ms	103×	body	320	valid
17.0ms	54×	body	160	valid
3.0ms	2×	body	2560	valid