Details

Time bar (total: 36.6s)

sample101.0ms

Algorithm
intervals
Results
65.0ms257×body80valid
4.0ms6×body320valid
4.0ms5×body640valid
2.0ms1×body1280valid

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))))))

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize64.0ms

Local error

Found 4 expressions with local error:

31.3b
(cos (- (* (/ K 2) (+ m n)) M))
0.0b
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
0.0b
(* (/ K 2) (+ m n))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
20×add-cube-cbrt
13×associate-*l*
12×prod-diff
10×times-frac
9×add-cbrt-cube add-exp-log
7×cos-sum
6×pow1 add-log-exp
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×fma-neg associate--l+
2×distribute-rgt-in frac-times sub-neg distribute-lft-in flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ fma-udef unswap-sqr
1×cos-diff cbrt-undiv flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 101
Calls
4 calls:
Slowest
48.0ms
(cos (- (* (/ K 2) (+ m n)) M))
35.0ms
(* (/ K 2) (+ m n))
10.0ms
(- (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)

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
214.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
70.0ms
(cos (- (* (/ K 2) (+ m n)) M))
61.0ms
(* (/ K 2) (+ m n))

simplify10.2s

Counts
78 → 113
Calls
78 calls:
Slowest
522.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
492.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
490.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
411.0ms
(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
321.0ms
(fma (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize45.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
Slowest
5.0ms
(- (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)

series438.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
229.0ms
(- (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)

simplify7.0s

Counts
31 → 47
Calls
31 calls:
Slowest
945.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
534.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
401.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
387.0ms
(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
350.0ms
(fma (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))

prune625.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize109.0ms

Local error

Found 4 expressions with local error:

31.1b
(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)

rewrite204.0ms

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
202.0ms
(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)

series363.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
363.0ms
(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)

simplify3.8s

Counts
25 → 68
Calls
25 calls:
Slowest
400.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
361.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos M))
339.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)))) (cos (- M)))
327.0ms
(* (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))))))
297.0ms
(* (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)))))

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.6b

localize126.0ms

Local error

Found 4 expressions with local error:

31.2b
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) (+ m n))) M))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite696.0ms

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
694.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) (+ m n))) M))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series341.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
341.0ms
(cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) (+ m n))) M))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify2.2s

Counts
22 → 68
Calls
22 calls:
Slowest
224.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
211.0ms
(* (cos (fma (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) (+ m n)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
206.0ms
(* (cos (* (* m (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2))))) (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))))) (cos (- (* (* n (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2))))) (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2)))) M)))
196.0ms
(* (cos (* (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) m) (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))))) (cos (- (* (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) n) (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2)))) M)))
195.0ms
(* (cos (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) m))) (cos (- (* (* (/ (cbrt K) (cbrt 2)) (/ (cbrt K) (cbrt 2))) (* (/ (cbrt K) (* (* (cbrt (cbrt 2)) (cbrt (cbrt 2))) (cbrt (cbrt 2)))) n)) M)))

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 1.6b

regimes743.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s8103×body80valid
484.0ms155×body640valid
198.0ms108×body1280valid
119.0ms109×body320valid
21.0ms49×body160valid
7.0ms4×body2560valid