Details

Time bar (total: 29.0s)

sample138.0ms

Algorithm
intervals
Results
82.0ms260×body80valid
9.0ms7×body640valid
7.0ms4×body1280valid
6.0ms6×body320valid
1.0ms2×body160valid

simplify295.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
295.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize50.0ms

Local error

Found 4 expressions with local error:

36.7b
(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)

rewrite73.0ms

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
37.0ms
(cos (- (* (/ K 2) (+ m n)) M))
17.0ms
(- (* (/ K 2) (+ m n)) M)
16.0ms
(* (/ K 2) (+ m n))
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series421.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
204.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
86.0ms
(cos (- (* (/ K 2) (+ m n)) M))
75.0ms
(- (* (/ K 2) (+ m n)) M)
56.0ms
(* (/ K 2) (+ m n))

simplify5.3s

Counts
63 → 104
Calls
63 calls:
Slowest
389.0ms
(* 2 (+ (* m m) (- (* n n) (* m n))))
298.0ms
(* (* (* (/ K 2) (/ K 2)) (/ K 2)) (* (* (+ m n) (+ m n)) (+ m n)))
271.0ms
(* K (+ (pow m 3) (pow n 3)))
245.0ms
(* (/ (* (* K K) K) (* (* 2 2) 2)) (* (* (+ m n) (+ m n)) (+ m n)))
231.0ms
(* K (- (* m m) (* n n)))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize55.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

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

series169.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
169.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify561.0ms

Counts
3 → 14
Calls
3 calls:
Slowest
241.0ms
(- (pow M 2) (+ (* m M) (* M n)))
192.0ms
(- (pow M 2) (+ (* m M) (* M n)))
127.0ms
(+ (* 1/2 (* m n)) (+ l (* 1/4 (pow m 2))))

prune239.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize76.0ms

Local error

Found 4 expressions with local error:

36.7b
(cos (- (* (/ K 2) (+ m n)) M))
32.8b
(posit16->real (real->posit16 (cos (- (* (/ K 2) (+ m n)) M))))
0.0b
(* (/ K 2) (+ m n))
0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
13×associate-*l* add-cube-cbrt
10×times-frac
9×add-cbrt-cube add-exp-log
7×cos-sum
6×pow1
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×prod-diff
2×distribute-rgt-in frac-times distribute-lft-in flip3-+ prod-exp associate--l+ associate-*r/ cbrt-unprod flip-+ unswap-sqr
1×cos-diff cbrt-undiv sub-neg div-exp pow-prod-down associate-*l/ *-commutative fma-udef div-inv remove-posit16 distribute-lft-out
Counts
4 → 82
Calls
4 calls:
Slowest
46.0ms
(cos (- (* (/ K 2) (+ m n)) M))
24.0ms
(* (/ K 2) (+ m n))
0.0ms
(posit16->real (real->posit16 (cos (- (* (/ K 2) (+ m n)) M))))
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
91.0ms
(cos (- (* (/ K 2) (+ m n)) M))
86.0ms
(posit16->real (real->posit16 (cos (- (* (/ K 2) (+ m n)) M))))
61.0ms
(* (/ K 2) (+ m n))

simplify4.4s

Counts
54 → 94
Calls
54 calls:
Slowest
337.0ms
(* 2 (+ (* m m) (- (* n n) (* m n))))
266.0ms
(* (* (* (/ K 2) (/ K 2)) (/ K 2)) (* (* (+ m n) (+ m n)) (+ m n)))
249.0ms
(* (/ (* (* K K) K) (* (* 2 2) 2)) (* (* (+ m n) (+ m n)) (+ m n)))
244.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
242.0ms
(* K (+ (pow m 3) (pow n 3)))

prune3.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize101.0ms

Local error

Found 4 expressions with local error:

44.4b
(cos (* (* (cbrt (- (* (/ K 2) (+ m n)) M)) (cbrt (- (* (/ K 2) (+ m n)) M))) (cbrt (- (* (/ K 2) (+ m n)) M))))
14.3b
(cbrt (- (* (/ K 2) (+ m n)) M))
14.3b
(cbrt (- (* (/ K 2) (+ m n)) M))
14.3b
(cbrt (- (* (/ K 2) (+ m n)) M))

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip--
Counts
4 → 58
Calls
4 calls:
Slowest
308.0ms
(cos (* (* (cbrt (- (* (/ K 2) (+ m n)) M)) (cbrt (- (* (/ K 2) (+ m n)) M))) (cbrt (- (* (/ K 2) (+ m n)) M))))
20.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))
19.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))
19.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
353.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))
352.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))
339.0ms
(cbrt (- (* (/ K 2) (+ m n)) M))
80.0ms
(cos (* (* (cbrt (- (* (/ K 2) (+ m n)) M)) (cbrt (- (* (/ K 2) (+ m n)) M))) (cbrt (- (* (/ K 2) (+ m n)) M))))

simplify4.9s

Counts
27 → 70
Calls
27 calls:
Slowest
738.0ms
(exp (* 1/3 (- (log 1/2) (+ (log (/ 1 m)) (log (/ 1 K))))))
275.0ms
(exp (* 1/3 (- (log 1/2) (+ (log (/ 1 m)) (log (/ 1 K))))))
273.0ms
(exp (* 1/3 (- (log 1/2) (+ (log (/ 1 m)) (log (/ 1 K))))))
252.0ms
(exp (* 1/3 (- (log 1/2) (+ (log (/ -1 m)) (log (/ -1 K))))))
243.0ms
(exp (* 1/3 (- (log 1/2) (+ (log (/ -1 m)) (log (/ -1 K))))))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes452.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.6s8085×body80valid
210.0ms106×body1280valid
156.0ms163×body640valid
127.0ms142×body320valid
26.0ms59×body160valid
7.0ms3×body2560valid