Details

sample40.0ms

Algorithm

intervals

Results

18.0ms	254×	body	80	valid
2.0ms	5×	body	1280	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15
done	5001	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
42×	`*-un-lft-identity` `prod-diff`
36×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`pow1` `add-exp-log` `fma-neg` `div-inv`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 124

Calls

4 calls:

22.0ms	(- (/ (* K (+ m n)) 2.0) M)
56.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(* K (+ m n))
35.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series415.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (/ (* K (+ m n)) 2.0) M)
267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(* K (+ m n))
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify58.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	612	1660
1	1907	1270
2	5003	1268
done	5003	1268

prune480.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite59.0ms

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:

58.0ms

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

series256.0ms

Counts

1 → 3

Calls

1 calls:

256.0ms

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

simplify41.0ms

Counts

25 → 25

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	159	174
1	445	168
2	1492	167
3	5001	162
done	5001	162

prune105.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-sum` `fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
3.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

series223.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
223.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify95.0ms

Counts

55 → 55

Iterations

Useful iterations: 4 (26.0ms)

Iter	Nodes	Cost
0	77	281
1	144	253
2	316	247
3	854	247
4	3641	244
5	5002	244
done	5002	244

prune351.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ K (* (cbrt 2.0) (cbrt 2.0)))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (- M)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`cbrt-prod`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `pow1/3` `div-exp`
1×	`cos-sum` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 59

Calls

4 calls:

9.0ms	(/ K (* (cbrt 2.0) (cbrt 2.0)))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
3.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (- M)))

series811.0ms

Counts

4 → 8

Calls

4 calls:

93.0ms	(/ K (* (cbrt 2.0) (cbrt 2.0)))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
718.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (- M)))

simplify42.0ms

Counts

67 → 67

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	177	452
1	505	400
2	1605	391
3	5002	391
done	5002	391

prune403.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes176.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10
done	23	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

633.0ms	8088×	body	80	valid
57.0ms	117×	body	1280	valid
47.0ms	139×	body	640	valid
26.0ms	108×	body	320	valid
9.0ms	56×	body	160	valid
2.0ms	3×	body	2560	valid