Details

Time bar (total: 47.0s)

sample104.0ms

Algorithm
intervals
Results
63.0ms260×body80valid
5.0ms7×body640valid
4.0ms4×body1280valid
4.0ms6×body320valid
1.0ms2×body160valid

simplify296.0ms

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))))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize42.0ms

Local error

Found 4 expressions with local error:

36.7b
(cos (- (/ (* (+ m n) K) 2) M))
0.2b
(/ (* (+ m n) K) 2)
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(* (+ m n) K)

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
13×pow1 add-cbrt-cube add-exp-log
12×add-cube-cbrt
10×associate-*l*
9×associate-*r*
8×swap-sqr difference-of-squares
7×times-frac
6×flip3-- associate-*l/ flip-- distribute-lft-out--
4×frac-times insert-posit16 add-log-exp
3×associate-/r* sub-neg prod-exp cbrt-unprod
2×distribute-rgt-in cbrt-undiv cos-sum distribute-lft-in flip3-+ div-exp pow-prod-down associate-*r/ *-commutative flip-+ unswap-sqr associate-/l/
1×pow2 cos-diff clear-num frac-2neg pow-plus pow-sqr pow-prod-up div-inv distribute-lft-out associate-/l*
Counts
4 → 106
Calls
4 calls:
Slowest
167.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
19.0ms
(cos (- (/ (* (+ m n) K) 2) M))
16.0ms
(/ (* (+ m n) K) 2)
14.0ms
(* (+ m n) K)

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
77.0ms
(cos (- (/ (* (+ m n) K) 2) M))
54.0ms
(/ (* (+ m n) K) 2)
41.0ms
(* (+ m n) K)

simplify9.1s

Counts
93 → 118
Calls
93 calls:
Slowest
592.0ms
(* (* (* (+ m n) (+ m n)) (+ m n)) (* (* K K) K))
450.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
426.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (/ (+ m n) 2) M))
380.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
366.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

Local error

Found 1 expressions with local error:

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

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
19×*-un-lft-identity
8×pow1 swap-sqr difference-of-squares
6×flip3-- associate-*r* associate-*l* flip-- distribute-lft-out--
5×add-cube-cbrt
4×frac-times times-frac
3×add-cbrt-cube add-exp-log
2×distribute-rgt-in sub-neg distribute-lft-in associate-*l/ associate-*r/
1×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod insert-posit16 add-log-exp unswap-sqr
Counts
1 → 49
Calls
1 calls:
Slowest
212.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series91.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
91.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify6.4s

Counts
55 → 52
Calls
55 calls:
Slowest
450.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
427.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (/ (+ m n) 2) M))
390.0ms
(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
375.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
353.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune805.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize86.0ms

Local error

Found 4 expressions with local error:

36.8b
(cos (- (/ (+ m n) (/ 2 K)) M))
0.2b
(/ (+ m n) (/ 2 K))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(- (/ (+ m n) (/ 2 K)) M)

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
104×times-frac
101×*-un-lft-identity
88×add-sqr-sqrt
57×add-cube-cbrt
14×distribute-lft-out
13×associate-/r*
11×pow1 add-cbrt-cube add-exp-log difference-of-squares
8×swap-sqr
7×flip3-- flip-- distribute-lft-out--
6×associate-*r* associate-*l* div-inv add-log-exp
4×frac-times sub-neg insert-posit16 associate-/l*
3×cbrt-undiv div-exp
2×distribute-rgt-in cos-sum distribute-lft-in associate-*l/ associate-*r/ associate-/l/
1×pow2 cos-diff clear-num frac-2neg flip3-+ pow-plus diff-log pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 164
Calls
4 calls:
Slowest
218.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
81.0ms
(cos (- (/ (+ m n) (/ 2 K)) M))
44.0ms
(- (/ (+ m n) (/ 2 K)) M)
31.0ms
(/ (+ m n) (/ 2 K))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
91.0ms
(- (/ (+ m n) (/ 2 K)) M)
71.0ms
(cos (- (/ (+ m n) (/ 2 K)) M))
54.0ms
(/ (+ m n) (/ 2 K))

simplify13.7s

Counts
200 → 176
Calls
200 calls:
Slowest
493.0ms
(/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt K) (cbrt K))))
436.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
407.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
399.0ms
(/ (+ m n) (cbrt (/ 2 K)))
384.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))

prune3.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize96.0ms

Local error

Found 4 expressions with local error:

36.7b
(cos (- (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (/ 2 K) (cbrt (+ m n)))) M))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 56
Calls
4 calls:
Slowest
97.0ms
(cos (- (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (/ 2 K) (cbrt (+ m n)))) M))
8.0ms
(cbrt (+ m n))
5.0ms
(cbrt (+ m n))
5.0ms
(cbrt (+ m n))

series731.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(cbrt (+ m n))
200.0ms
(cbrt (+ m n))
167.0ms
(cbrt (+ m n))
156.0ms
(cos (- (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (/ 2 K) (cbrt (+ m n)))) M))

simplify3.0s

Counts
33 → 68
Calls
33 calls:
Slowest
482.0ms
(- (+ (* 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))))
434.0ms
(- (+ (* 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))))
422.0ms
(- (+ (* 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))))
166.0ms
(* (cos (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (/ 2 K) (cbrt (+ m n))))) (cos (- M)))
162.0ms
(* (cos (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ (/ 2 K) (cbrt (+ m n))))) (cos (- M)))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes449.0ms

Accuracy

0% (0.2b remaining)

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

bsearch6.0ms

end1.0ms

sample3.7s

Algorithm
intervals
Results
2.7s8085×body80valid
312.0ms163×body640valid
145.0ms106×body1280valid
109.0ms142×body320valid
31.0ms59×body160valid
5.0ms3×body2560valid