Details

Time bar (total: 28.0s)

sample125.0ms

Algorithm
intervals
Results
78.0ms267×body80valid
9.0ms7×body640valid
8.0ms5×body1280valid
4.0ms4×body320valid
2.0ms4×body160valid

simplify245.0ms

Calls
1 calls:
Slowest
245.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize44.0ms

Local error

Found 4 expressions with local error:

32.5b
(cos (- (/ K (/ 2 (+ m n))) M))
0.2b
(/ K (/ 2 (+ m n)))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(/ 2 (+ m n))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 associate-/r*
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×flip3-- add-cbrt-cube add-exp-log flip--
5×associate-/r/
4×frac-times insert-posit16 add-log-exp
3×sub-neg associate-*r* associate-*l* div-inv
2×distribute-rgt-in cos-sum clear-num frac-2neg distribute-lft-in flip3-+ associate-*l/ associate-*r/ flip-+
1×pow2 cos-diff pow-plus pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
47.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
6.0ms
(cos (- (/ K (/ 2 (+ m n))) M))
1.0ms
(/ 2 (+ m n))
1.0ms
(/ K (/ 2 (+ m n)))

series195.0ms

Calls
4 calls:
Slowest
63.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
62.0ms
(cos (- (/ K (/ 2 (+ m n))) M))
39.0ms
(/ K (/ 2 (+ m n)))
31.0ms
(/ 2 (+ m n))

simplify5.6s

Calls
54 calls:
Slowest
481.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
432.0ms
(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
429.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
389.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
300.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 flip3-- flip--
5×add-sqr-sqrt sub-neg
4×distribute-rgt-in frac-times *-un-lft-identity distribute-lft-in add-cbrt-cube add-exp-log add-cube-cbrt associate--r+ add-log-exp
3×associate-*r* associate-*l*
2×associate-*l/ associate-*r/ insert-posit16
1×pow2 pow-plus diff-log pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod difference-of-squares
Calls
2 calls:
Slowest
19.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
6.0ms
(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))

series134.0ms

Calls
2 calls:
Slowest
73.0ms
(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
61.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify6.3s

Calls
40 calls:
Slowest
527.0ms
(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
487.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
406.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
378.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
316.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune916.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize28.0ms

Local error

Found 4 expressions with local error:

32.8b
(cos (- (/ K (/ (/ 2 (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 flip-+
2×cos-sum
1×cos-diff sub-neg
Calls
4 calls:
Slowest
12.0ms
(cos (- (/ K (/ (/ 2 (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))

series550.0ms

Calls
4 calls:
Slowest
161.0ms
(cbrt (+ m n))
155.0ms
(cbrt (+ m n))
128.0ms
(cbrt (+ m n))
105.0ms
(cos (- (/ K (/ (/ 2 (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))

simplify2.0s

Calls
30 calls:
Slowest
333.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
321.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
293.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
180.0ms
(* (cos (/ K (/ (/ 2 (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))))) (cos (- M)))
121.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

30.2b
(cos (- (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))
0.6b
(cbrt (- m))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 cbrt-div add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×cos-sum flip3-+ flip-+
1×cos-diff neg-mul-1 sub-neg
Calls
4 calls:
Slowest
6.0ms
(cos (- (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))
1.0ms
(cbrt (- m))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))

series915.0ms

Calls
4 calls:
Slowest
322.0ms
(cos (- (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n)))) M))
307.0ms
(cbrt (- m))
145.0ms
(cbrt (+ m n))
141.0ms
(cbrt (+ m n))

simplify2.2s

Calls
29 calls:
Slowest
321.0ms
(* (cos (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n))))) (cos (- M)))
304.0ms
(* (cos (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n))))) (cos M))
264.0ms
(* (cos (/ K (/ (/ 2 (* (* (cbrt (- m)) (cbrt -1)) (cbrt (+ m n)))) (cbrt (+ m n))))) (cos (- M)))
261.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
257.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes386.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.5s8140×body80valid
214.0ms162×body640valid
175.0ms116×body1280valid
147.0ms96×body320valid
24.0ms57×body160valid
13.0ms7×body2560valid