Details

sample92.0ms

Algorithm

intervals

Results

44.0ms	265×	body	80	valid
5.0ms	5×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (188.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	220	29
4	680	28
5	3210	28
done	5001	28

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

40.0ms	(* K (+ m n))
819.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
118.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
73.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

49.0ms	(* K (+ m n))
378.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
527.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
131.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.6s

Counts

130 → 130

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	348	2962
1	765	2453
2	2287	2139
done	5002	2013

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite953.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
12×	`add-cube-cbrt` `unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
7×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `pow-unpow` `distribute-lft-out--`
2×	`expm1-log1p-u` `times-frac` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `diff-log` `pow-exp` `flip-+`

Counts

2 → 60

Calls

2 calls:

823.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
125.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series866.0ms

Counts

2 → 6

Calls

2 calls:

366.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
500.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.2s

Counts

66 → 66

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	144	1073
1	361	956
2	1121	889
done	5000	876

prune725.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize104.0ms

Local error

Found 4 expressions with local error:

17.7b	(cbrt (* K (+ m n)))
17.7b	(cbrt (* K (+ m n)))
17.7b	(cbrt (* K (+ m n)))
37.5b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

14.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
118.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series787.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt (* K (+ m n)))
217.0ms	(cbrt (* K (+ m n)))
214.0ms	(cbrt (* K (+ m n)))
131.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	228	3327
1	430	2926
2	879	1839
3	2450	1392
done	5000	1266

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize130.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ K (sqrt 2.0))
0.5b	(/ K (sqrt 2.0))
37.0b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
37.0b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

12.0ms	(/ K (sqrt 2.0))
12.0ms	(/ K (sqrt 2.0))
5.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
5.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series1.0s

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ K (sqrt 2.0))
106.0ms	(/ K (sqrt 2.0))
398.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
401.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify1.7s

Counts

114 → 114

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	117	1264
1	197	1180
2	455	1104
3	1469	987
done	5000	984

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes713.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	19
1	20	19
done	20	19

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.2s	8091×	body	80	valid
692.0ms	119×	body	1280	valid
194.0ms	165×	body	640	valid
74.0ms	58×	body	160	valid
60.0ms	98×	body	320	valid
3.0ms	2×	body	2560	valid