Details

sample134.0ms

Algorithm

intervals

Results

80.0ms	261×	body	80	valid
9.0ms	5×	body	1280	valid
4.0ms	3×	body	640	valid
4.0ms	4×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	3132
4	821
3	260
2	102
1	51
0	21

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* K (/ (+ m n) 2)) M)
0.0b	(* K (/ (+ m n) 2))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
37.1b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `prod-diff` `add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `flip3--` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 84

Calls

4 calls:

21.0ms	(- (* K (/ (+ m n) 2)) M)
32.0ms	(* K (/ (+ m n) 2))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
55.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series391.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* K (/ (+ m n) 2)) M)
50.0ms	(* K (/ (+ m n) 2))
196.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
69.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
3	3196
2	1038
1	409
0	188

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize41.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

0.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series212.0ms

Counts

1 → 3

Calls

1 calls:

212.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify3.7s

Counts

14 → 14

Iterations

Iter	Nodes
5	6545
4	1190
3	343
2	130
1	64
0	33

prune220.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
37.3b	(cos (- (* (* K (* (/ (cbrt (+ m n)) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `prod-diff` `flip-+` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 67

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
525.0ms	(cos (- (* (* K (* (/ (cbrt (+ m n)) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt (+ m n))
226.0ms	(cbrt (+ m n))
184.0ms	(cbrt (+ m n))
451.0ms	(cos (- (* (* K (* (/ (cbrt (+ m n)) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

simplify1.2s

Counts

79 → 79

Iterations

Iter	Nodes
4	2804
3	1186
2	525
1	257
0	133

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize81.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
37.2b	(cos (- (* (* K (* (/ (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
16×	`cbrt-prod`
12×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `flip3-+` `add-cube-cbrt` `flip-+`
5×	`cos-sum`
4×	`expm1-log1p-u` `frac-times` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
2×	`associate-l/` `associate-r/` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 73

Calls

4 calls:

3.0ms	(cbrt (+ m n))
4.0ms	(cbrt (cbrt (+ m n)))
10.0ms	(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
1.3s	(cos (- (* (* K (* (/ (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

series1.4s

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (+ m n))
311.0ms	(cbrt (cbrt (+ m n)))
460.0ms	(cbrt (* (cbrt (+ m n)) (cbrt (+ m n))))
445.0ms	(cos (- (* (* K (* (/ (* (cbrt (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (cbrt (+ m n)))) (sqrt 2)) (cbrt (+ m n)))) (/ (cbrt (+ m n)) (sqrt 2))) M))

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
3	2670
2	1004
1	441
0	230

prune2.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes490.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.5s	8128×	body	80	valid
203.0ms	146×	body	640	valid
146.0ms	128×	body	1280	valid
58.0ms	94×	body	320	valid
26.0ms	56×	body	160	valid
8.0ms	4×	body	2560	valid