Details

sample89.0ms

Algorithm

intervals

Results

47.0ms	263×	body	80	valid
5.0ms	5×	body	1280	valid
5.0ms	6×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1428
4	534
3	208
2	93
1	50
0	21

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (/ (* (+ m n) K) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.1b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

51×	`prod-diff`
50×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
41×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
10×	`fma-neg`
8×	`add-log-exp`
7×	`div-inv`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `sub-neg` `distribute-lft-out--`
2×	`flip3--` `diff-log` `flip--`
1×	`cos-diff` `pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

5.0ms	(- (fabs (- m n)) l)
17.0ms	(- (/ (* (+ m n) K) 2.0) M)
66.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
31.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series569.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (fabs (- m n)) l)
69.0ms	(- (/ (* (+ m n) K) 2.0) M)
371.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
91.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	3465
2	1230
1	662
0	326

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`pow1` `pow-unpow` `fma-neg` `add-exp-log` `difference-of-squares`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `pow-pow` `times-frac` `flip3--` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 50

Calls

2 calls:

5.0ms	(- (fabs (- m n)) l)
62.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series386.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(- (fabs (- m n)) l)
356.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	4446
3	1605
2	625
1	308
0	132

prune386.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize104.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
30.3b	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (cbrt 2.0)) (- M)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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)
2.0ms	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (cbrt 2.0)) (- M)))

series262.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
261.0ms	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (cbrt 2.0)) (- M)))

simplify3.8s

Counts

55 → 55

Iterations

Iter	Nodes
done	5143
6	4003
5	927
4	357
3	214
2	132
1	80
0	51

prune573.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (cbrt 2.0))
1.0b	(cbrt (cbrt 2.0))
1.0b	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
30.0b	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
23×	`pow1`
14×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `pow1/3` `add-cube-cbrt`
9×	`associate-r` `add-exp-log` `pow-prod-up`
6×	`pow-plus`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`cos-sum` `associate-l` `pow3` `*-commutative` `fma-udef`

Counts

4 → 83

Calls

4 calls:

1.0ms	(cbrt (cbrt 2.0))
1.0ms	(cbrt (cbrt 2.0))
38.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
2.0ms	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

series286.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt (cbrt 2.0))
0.0ms	(cbrt (cbrt 2.0))
0.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
286.0ms	(cos (fma (/ (+ m n) (* (cbrt 2.0) (cbrt 2.0))) (/ K (* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))) (- M)))

simplify2.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5361
4	2713
3	915
2	413
1	193
0	99

prune716.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

regimes412.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.0s	8113×	body	80	valid
176.0ms	139×	body	640	valid
119.0ms	139×	body	1280	valid
47.0ms	103×	body	320	valid
17.0ms	56×	body	160	valid
3.0ms	2×	body	2560	valid