Details

sample105.0ms

Algorithm

intervals

Results

62.0ms	260×	body	80	valid
6.0ms	6×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid

simplify7.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4953
5	1387
4	532
3	208
2	93
1	50
0	21

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ n m) 2.0) M)
0.0b	(* (+ n m) K)
0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)
39.2b	(cos (- (/ (* (+ n m) K) 2.0) M))

rewrite376.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

118.0ms	(- (/ (+ n m) 2.0) M)
42.0ms	(* (+ n m) K)
125.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
72.0ms	(cos (- (/ (* (+ n m) K) 2.0) M))

series684.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (/ (+ n m) 2.0) M)
46.0ms	(* (+ n m) K)
463.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
122.0ms	(cos (- (/ (* (+ n m) K) 2.0) M))

simplify5.5s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
3	4926
2	1676
1	759
0	359

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize66.0ms

Local error

Found 3 expressions with local error:

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

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
57×	`prod-diff`
50×	`times-frac`
16×	`fma-neg`
14×	`distribute-lft-out`
11×	`associate-+l+`
10×	`add-log-exp`
6×	`unpow-prod-down`
5×	`fma-def` `difference-of-squares`
4×	`pow1` `add-exp-log` `div-inv` `distribute-lft-out--`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `sum-log`
1×	`+-commutative` `pow-to-exp` `associate-+l-` `flip3--` `pow-pow` `flip3-+` `pow-exp` `flip--` `flip-+` `sqr-pow`

Counts

3 → 136

Calls

3 calls:

398.0ms	(+ (- l (fabs (- m n))) (pow (- (/ (+ n m) 2.0) M) 2.0))
117.0ms	(- (/ (+ n m) 2.0) M)
155.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)

series1.1s

Counts

3 → 9

Calls

3 calls:

452.0ms	(+ (- l (fabs (- m n))) (pow (- (/ (+ n m) 2.0) M) 2.0))
87.0ms	(- (/ (+ n m) 2.0) M)
539.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)

simplify4.7s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
3	4268
2	1280
1	549
0	225

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize114.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)
0.1b	(exp (cos (- (/ (* (+ n m) K) 2.0) M)))
0.5b	(log (exp (cos (- (/ (* (+ n m) K) 2.0) M))))
39.2b	(cos (- (/ (* (+ n m) K) 2.0) M))

rewrite458.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cos-sum`
63×	`prod-diff`
53×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
46×	`exp-diff`
28×	`times-frac`
23×	`log-div`
9×	`div-inv`
6×	`pow1` `unpow-prod-down` `exp-prod`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`cos-diff` `sub-neg` `pow-unpow`
2×	`exp-sum` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `rem-exp-log` `distribute-lft-out--` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

120.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
82.0ms	(exp (cos (- (/ (* (+ n m) K) 2.0) M)))
149.0ms	(log (exp (cos (- (/ (* (+ n m) K) 2.0) M))))
91.0ms	(cos (- (/ (* (+ n m) K) 2.0) M))

series997.0ms

Counts

4 → 12

Calls

4 calls:

502.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
211.0ms	(exp (cos (- (/ (* (+ n m) K) 2.0) M)))
125.0ms	(log (exp (cos (- (/ (* (+ n m) K) 2.0) M))))
159.0ms	(cos (- (/ (* (+ n m) K) 2.0) M))

simplify2.9s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
3	2331
2	1150
1	691
0	364

prune2.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize97.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ n m))
0.5b	(cbrt (+ n m))
0.5b	(cbrt (+ n m))
39.3b	(cos (- (/ (* (* (cbrt (+ n m)) (cbrt (+ n m))) (* (cbrt (+ n m)) K)) 2.0) M))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod`
9×	`times-frac`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `div-inv` `distribute-lft-out`
1×	`cos-diff` `sub-neg`

Counts

4 → 81

Calls

4 calls:

8.0ms	(cbrt (+ n m))
7.0ms	(cbrt (+ n m))
7.0ms	(cbrt (+ n m))
304.0ms	(cos (- (/ (* (* (cbrt (+ n m)) (cbrt (+ n m))) (* (cbrt (+ n m)) K)) 2.0) M))

series970.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (+ n m))
237.0ms	(cbrt (+ n m))
284.0ms	(cbrt (+ n m))
220.0ms	(cos (- (/ (* (* (cbrt (+ n m)) (cbrt (+ n m))) (* (cbrt (+ n m)) K)) 2.0) M))

simplify3.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
3	2049
2	831
1	442
0	233

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes817.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	19

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.7s	8083×	body	80	valid
236.0ms	139×	body	1280	valid
127.0ms	103×	body	320	valid
123.0ms	145×	body	640	valid
21.0ms	54×	body	160	valid
3.0ms	2×	body	2560	valid