Details

Time bar (total: 1.0m)

sample101.0ms

Algorithm
intervals
Results
65.0ms262×body80valid
5.0ms6×body640valid
4.0ms6×body320valid
2.0ms2×body1280valid
1.0ms2×body160valid

simplify335.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
335.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize38.0ms

Local error

Found 4 expressions with local error:

32.1b
(cos (- (* (/ K 2) (+ m n)) M))
0.0b
(* (/ K 2) (+ m n))
0.0b
(- (* (/ K 2) (+ m n)) M)
0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

rewrite427.0ms

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
393.0ms
(cos (- (* (/ K 2) (+ m n)) M))
19.0ms
(* (/ K 2) (+ m n))
13.0ms
(- (* (/ K 2) (+ m n)) M)
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
81.0ms
(- (* (/ K 2) (+ m n)) M)
71.0ms
(* (/ K 2) (+ m n))
68.0ms
(cos (- (* (/ K 2) (+ m n)) M))

simplify5.1s

Counts
63 → 104
Calls
63 calls:
Slowest
298.0ms
(* 2 (+ (* m m) (- (* n n) (* m n))))
297.0ms
(* K (+ (pow m 3) (pow n 3)))
245.0ms
(- (pow M 2) (+ (* m M) (* M n)))
242.0ms
(* (/ (* (* K K) K) (* (* 2 2) 2)) (* (* (+ m n) (+ m n)) (+ m n)))
227.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize60.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b
(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))
0.0b
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt *-un-lft-identity
55×add-cube-cbrt
48×exp-sum
45×times-frac prod-diff
15×associate-/r*
6×fma-udef pow-flip
5×exp-prod sub-neg add-cbrt-cube associate--l+ add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u associate-/l*
2×div-exp distribute-lft-out-- difference-of-squares
1×cbrt-undiv rec-exp clear-num frac-2neg flip3-- exp-diff diff-log 1-exp associate-/r/ div-inv flip-- inv-pow
Counts
3 → 129
Calls
3 calls:
Slowest
24.0ms
(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))
7.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series648.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
245.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
209.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
193.0ms
(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))

simplify34.5s

Counts
151 → 138
Calls
151 calls:
Slowest
798.0ms
(/ 1 (exp (fma (* (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (fabs (- m n)) 1)))))
661.0ms
(/ (* (* 1 1) 1) (* (* (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))) (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))) (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))))
546.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
545.0ms
(- (/ 1 (exp (- (fabs (- m n))))) (+ (/ l (exp (- (fabs (- m n))))) (* 1/4 (/ (pow m 2) (exp (- (fabs (- m n))))))))
515.0ms
(- (log 1) (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize80.0ms

Local error

Found 4 expressions with local error:

32.0b
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod cos-sum
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×distribute-rgt-in expm1-log1p-u pow1 distribute-lft-in add-cbrt-cube associate--l+ add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 prod-diff
1×cos-diff sub-neg
Counts
4 → 62
Calls
4 calls:
Slowest
240.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series305.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
305.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify4.2s

Counts
25 → 68
Calls
25 calls:
Slowest
435.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos M))
396.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
396.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
371.0ms
(* (cos (fma (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
323.0ms
(* (cos (fma (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.2b

localize80.0ms

Local error

Found 4 expressions with local error:

32.0b
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod cos-sum
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×distribute-rgt-in expm1-log1p-u pow1 distribute-lft-in add-cbrt-cube associate--l+ add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 prod-diff
1×cos-diff sub-neg
Counts
4 → 62
Calls
4 calls:
Slowest
190.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series780.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
780.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n))) M))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify3.5s

Counts
22 → 68
Calls
22 calls:
Slowest
400.0ms
(* (cos (fma (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
386.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos M))
382.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
372.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
315.0ms
(* (cos (fma (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.2b

regimes504.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.8s8097×body80valid
192.0ms114×body1280valid
160.0ms164×body640valid
108.0ms103×body320valid
20.0ms43×body160valid
8.0ms4×body2560valid