Details

Time bar (total: 27.0s)

sample102.0ms

Algorithm
intervals
Results
57.0ms253×body80valid
9.0ms10×body640valid
3.0ms5×body320valid
3.0ms2×body1280valid
0.0ms1×body160valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5005
53184
4821
3262
2104
151
021

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b
(* K (+ m n))
0.1b
(pow (- (/ (+ m n) 2) M) 2)
32.6b
(cos (- (/ (* K (+ m n)) 2) M))

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
204×add-sqr-sqrt
173×*-un-lft-identity
160×prod-diff
83×add-cube-cbrt
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
53×difference-of-squares
45×distribute-lft-out--
26×fma-neg
23×cos-sum
22×times-frac
14×add-log-exp
13×unpow2 sqr-pow
11×associate--r+
7×pow1 add-exp-log
6×neg-mul-1 add-cbrt-cube diff-log
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×pow-unpow sub-neg associate-*l* div-inv
2×neg-log associate-*r/
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ flip3-- pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out associate--r- unswap-sqr
Counts
4 → 276
Calls
4 calls:
858.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
28.0ms
(* K (+ m n))
63.0ms
(pow (- (/ (+ m n) 2) M) 2)
21.0ms
(cos (- (/ (* K (+ m n)) 2) M))

series417.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
37.0ms
(* K (+ m n))
81.0ms
(pow (- (/ (+ m n) 2) M) 2)
75.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify1.7s

Counts
288 → 288
Iterations
IterNodes
done5010
22141
11039
0474

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(- l (fabs (- m n)))
0.0b
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.1b
(pow (- (/ (+ m n) 2) M) 2)

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
352×add-sqr-sqrt
299×*-un-lft-identity
278×prod-diff
138×unpow-prod-down
133×exp-sum
127×add-cube-cbrt
125×distribute-rgt-neg-in
121×distribute-lft-neg-in
101×difference-of-squares
88×distribute-lft-out--
29×fma-neg
27×add-log-exp
23×times-frac unpow2 sqr-pow
13×diff-log
11×neg-mul-1 associate--r+
8×exp-prod
5×pow1 add-exp-log rem-exp-log
4×expm1-log1p-u sub-neg add-cbrt-cube neg-log insert-posit16 log1p-expm1-u
3×pow-unpow
2×flip3-- flip-- associate--r-
1×associate--l- neg-sub0 pow-to-exp pow-pow exp-diff pow-exp
Counts
4 → 402
Calls
4 calls:
10.0ms
(- l (fabs (- m n)))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
980.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
47.0ms
(pow (- (/ (+ m n) 2) M) 2)

series549.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(- l (fabs (- m n)))
172.0ms
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
239.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
112.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify1.9s

Counts
414 → 414
Iterations
IterNodes
done5001
21992
1873
0415

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

localize56.0ms

Local error

Found 4 expressions with local error:

13.8b
(cbrt (* K (+ m n)))
13.8b
(cbrt (* K (+ m n)))
13.8b
(cbrt (* K (+ m n)))
32.4b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
6×cbrt-div associate-*r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+ div-inv
1×cos-diff sub-neg
Counts
4 → 76
Calls
4 calls:
6.0ms
(cbrt (* K (+ m n)))
9.0ms
(cbrt (* K (+ m n)))
9.0ms
(cbrt (* K (+ m n)))
46.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

series565.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt (* K (+ m n)))
149.0ms
(cbrt (* K (+ m n)))
158.0ms
(cbrt (* K (+ m n)))
74.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify2.1s

Counts
88 → 88
Iterations
IterNodes
done5000
31772
2759
1430
0230

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.2b

localize87.0ms

Local error

Found 4 expressions with local error:

12.6b
(cbrt (* K n))
13.8b
(cbrt (* K (+ m n)))
13.8b
(cbrt (* K (+ m n)))
28.4b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K n))) (cbrt (* K (+ m n)))) 2) M))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×expm1-log1p-u pow1 cbrt-div add-cbrt-cube associate-*r/ add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 div-inv
2×flip3-+ flip-+
1×cos-diff sub-neg
Counts
4 → 74
Calls
4 calls:
3.0ms
(cbrt (* K n))
8.0ms
(cbrt (* K (+ m n)))
5.0ms
(cbrt (* K (+ m n)))
33.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K n))) (cbrt (* K (+ m n)))) 2) M))

series1.1s

Counts
4 → 12
Calls
4 calls:
78.0ms
(cbrt (* K n))
623.0ms
(cbrt (* K (+ m n)))
164.0ms
(cbrt (* K (+ m n)))
246.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K n))) (cbrt (* K (+ m n)))) 2) M))

simplify2.0s

Counts
86 → 86
Iterations
IterNodes
done5001
32294
2924
1508
0265

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.2b

regimes888.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.8s8100×body80valid
178.0ms186×body640valid
175.0ms134×body1280valid
77.0ms107×body320valid
32.0ms67×body160valid
5.0ms2×body2560valid