Details

sample130.0ms

Algorithm

intervals

Results

84.0ms	257×	body	80	valid
9.0ms	6×	body	1280	valid
9.0ms	8×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid

simplify994.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(* K (/ (+ m n) 2))
37.2b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

6.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
16.0ms	(* K (/ (+ m n) 2))
35.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series536.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
198.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
64.0ms	(* K (/ (+ m n) 2))
62.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.4s

Counts

107 → 107

Iterations

Iter	Nodes
3	3885
2	1217
1	470
0	220

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize58.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

10.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
1.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series450.0ms

Counts

2 → 6

Calls

2 calls:

203.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
247.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify5.0s

Counts

47 → 47

Iterations

Iter	Nodes
4	6100
3	1469
2	437
1	184
0	88

prune735.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize85.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
37.4b	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (cbrt 2))) M))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
218.0ms	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (cbrt 2))) M))

series335.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
335.0ms	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (cbrt 2))) M))

simplify2.0s

Counts

64 → 64

Iterations

Iter	Nodes
5	4052
4	1536
3	616
2	284
1	172
0	103

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.3b

localize99.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
37.4b	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2))))) M))

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
316.0ms	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2))))) M))

series372.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
372.0ms	(cos (- (* (/ K (* (/ (cbrt 2) (cbrt (+ m n))) (/ (cbrt 2) (cbrt (+ m n))))) (/ (cbrt (+ m n)) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2))))) M))

simplify756.0ms

Counts

64 → 64

Iterations

Iter	Nodes
4	2103
3	636
2	263
1	155
0	95

prune2.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.3b

regimes548.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.6s	8120×	body	80	valid
206.0ms	164×	body	640	valid
169.0ms	116×	body	1280	valid
65.0ms	96×	body	320	valid
24.0ms	54×	body	160	valid