Details

Time bar (total: 19.2s)

sample83.0ms

Algorithm
intervals
Results
56.0ms258×body80valid
3.0ms3×body640valid
1.0ms3×body160valid
1.0ms1×body1280valid

simplify305.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
305.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize47.0ms

Local error

Found 4 expressions with local error:

35.0b
(cos (- (* (/ K 2) (+ m n)) M))
0.0b
(* (/ K 2) (+ m n))
0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b
(- (* (/ K 2) (+ m n)) M)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×associate-*l*
10×times-frac
9×add-cbrt-cube add-exp-log
7×cos-sum
6×pow1 prod-diff add-log-exp
4×expm1-log1p-u associate-*r* associate--l+ insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×frac-times sub-neg flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ unswap-sqr
1×cos-diff cbrt-undiv flip3-- fma-neg diff-log div-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv flip-- distribute-lft-out
Counts
4 → 92
Calls
4 calls:
Slowest
38.0ms
(cos (- (* (/ K 2) (+ m n)) M))
34.0ms
(* (/ K 2) (+ m n))
15.0ms
(- (* (/ K 2) (+ m n)) M)
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
81.0ms
(cos (- (* (/ K 2) (+ m n)) M))
67.0ms
(- (* (/ K 2) (+ m n)) M)
51.0ms
(* (/ K 2) (+ m n))

simplify5.5s

Counts
63 → 104
Calls
63 calls:
Slowest
345.0ms
(* 2 (+ (* m m) (- (* n n) (* m n))))
292.0ms
(* K (+ (pow m 3) (pow n 3)))
292.0ms
(- (pow M 2) (+ (* m M) (* M n)))
278.0ms
(* (/ (* (* K K) K) (* (* 2 2) 2)) (* (* (+ m n) (+ m n)) (+ m n)))
261.0ms
(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize55.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 11
Calls
1 calls:
Slowest
1.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series234.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
234.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify657.0ms

Counts
3 → 14
Calls
3 calls:
Slowest
267.0ms
(- (pow M 2) (+ (* m M) (* M n)))
228.0ms
(- (pow M 2) (+ (* m M) (* M n)))
160.0ms
(+ (* 1/2 (* m n)) (+ l (* 1/4 (pow m 2))))

prune261.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize95.0ms

Local error

Found 4 expressions with local error:

28.3b
(sin (* m (/ K 2)))
28.2b
(cos (* m (/ K 2)))
25.4b
(sin (- (* n (/ K 2)) M))
25.0b
(cos (- (* n (/ K 2)) M))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity prod-diff add-cube-cbrt
5×cos-sum sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff
Counts
4 → 52
Calls
4 calls:
Slowest
33.0ms
(sin (- (* n (/ K 2)) M))
24.0ms
(cos (- (* n (/ K 2)) M))
14.0ms
(sin (* m (/ K 2)))
13.0ms
(cos (* m (/ K 2)))

series143.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
60.0ms
(sin (- (* n (/ K 2)) M))
38.0ms
(cos (- (* n (/ K 2)) M))
26.0ms
(sin (* m (/ K 2)))
18.0ms
(cos (* m (/ K 2)))

simplify1.1s

Counts
24 → 64
Calls
24 calls:
Slowest
99.0ms
(* (cos (fma n (/ K 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
91.0ms
(* (sin (fma n (/ K 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
81.0ms
(* (cos (fma n (/ K 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
66.0ms
(* (cos (fma n (/ K 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
62.0ms
(* (sin (fma n (/ K 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize159.0ms

Local error

Found 4 expressions with local error:

28.9b
(sin (* n (/ K 2)))
28.7b
(cos (* n (/ K 2)))
28.3b
(sin (* m (/ K 2)))
28.2b
(cos (* m (/ K 2)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
Slowest
15.0ms
(sin (* n (/ K 2)))
15.0ms
(sin (* m (/ K 2)))
15.0ms
(cos (* n (/ K 2)))
14.0ms
(cos (* m (/ K 2)))

series101.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
35.0ms
(sin (* n (/ K 2)))
29.0ms
(sin (* m (/ K 2)))
19.0ms
(cos (* n (/ K 2)))
19.0ms
(cos (* m (/ K 2)))

simplify291.0ms

Counts
12 → 52
Calls
12 calls:
Slowest
35.0ms
(sin (* 1/2 (* K n)))
31.0ms
(cos (* 1/2 (* m K)))
30.0ms
(sin (* 1/2 (* K n)))
30.0ms
(cos (* 1/2 (* K n)))
30.0ms
(sin (* 1/2 (* m K)))

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes460.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.1s8126×body80valid
161.0ms111×body1280valid
157.0ms139×body640valid
90.0ms111×body320valid
31.0ms54×body160valid
6.0ms3×body2560valid