Details

Time bar (total: 1.0m)

sample136.0ms

Algorithm
intervals
Results
84.0ms253×body80valid
12.0ms7×body1280valid
5.0ms5×body640valid
2.0ms1×body2560valid
2.0ms3×body320valid
2.0ms3×body160valid

simplify247.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
246.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize58.0ms

Local error

Found 4 expressions with local error:

35.7b
(cos (- (/ (* (+ m n) K) 2) M))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(- (/ (* (+ m n) K) 2) M)
0.0b
(/ (* (+ m n) K) 2)

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
26×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×difference-of-squares
8×swap-sqr
7×times-frac flip3-- flip-- distribute-lft-out--
6×associate-*r* associate-*l* add-log-exp
4×frac-times sub-neg associate-*l/ insert-posit16
3×associate-/r*
2×distribute-rgt-in cbrt-undiv cos-sum distribute-lft-in div-exp prod-exp associate-*r/ cbrt-unprod associate-/l/
1×pow2 cos-diff clear-num frac-2neg flip3-+ pow-plus diff-log pow-prod-down pow-sqr *-commutative pow-prod-up flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
206.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
25.0ms
(cos (- (/ (* (+ m n) K) 2) M))
24.0ms
(- (/ (* (+ m n) K) 2) M)
15.0ms
(/ (* (+ m n) K) 2)

series280.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(- (/ (* (+ m n) K) 2) M)
80.0ms
(cos (- (/ (* (+ m n) K) 2) M))
76.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
40.0ms
(/ (* (+ m n) K) 2)

simplify9.2s

Counts
86 → 111
Calls
86 calls:
Slowest
433.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
413.0ms
(* (sqrt (- (/ (+ m n) 2) M)) (sqrt (- (/ (+ m n) 2) M)))
405.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))
369.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
368.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (/ (+ m n) 2) M))

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize53.0ms

Local error

Found 3 expressions with local error:

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

rewrite856.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
31×*-un-lft-identity
26×flip3-- flip--
17×add-cube-cbrt
16×times-frac frac-add
12×frac-times
11×pow1
8×swap-sqr add-log-exp difference-of-squares
7×add-cbrt-cube
6×associate-*r* associate-*l* associate-*l/ associate-*r/ add-exp-log distribute-lft-out--
5×sub-neg
4×distribute-rgt-in associate-+l+ associate-/r* distribute-lft-in exp-sum pow-flip
3×exp-prod insert-posit16 associate-/l*
2×associate-+r+ associate-+r- sum-log div-exp
1×pow2 cbrt-undiv +-commutative rec-exp clear-num frac-2neg flip3-+ pow-plus exp-diff diff-log 1-exp pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv inv-pow unswap-sqr
Counts
3 → 125
Calls
3 calls:
Slowest
475.0ms
(/ 1 (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))
247.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
130.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))

series482.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
224.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
177.0ms
(/ 1 (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))
82.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify30.4s

Counts
140 → 134
Calls
140 calls:
Slowest
946.0ms
(+ (* (* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
873.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (pow l 3) (pow (fabs (- m n)) 3))))
728.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
659.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ l (fabs (- m n)))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (* l l) (* (fabs (- m n)) (fabs (- m n))))))
655.0ms
(+ (* (* (- (/ (+ m n) 2) M) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (- (pow l 3) (pow (fabs (- m n)) 3))))

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize49.0ms

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)) l))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
22×*-un-lft-identity
9×pow1 difference-of-squares
8×swap-sqr
7×flip3-- flip-- distribute-lft-out-- add-log-exp
6×associate-*r* associate-*l* add-cube-cbrt
4×frac-times times-frac add-cbrt-cube add-exp-log
3×sub-neg
2×distribute-rgt-in distribute-lft-in diff-log associate-*l/ associate-*r/ insert-posit16
1×pow2 sum-log pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod associate--r+ unswap-sqr
Counts
2 → 66
Calls
2 calls:
Slowest
222.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
151.0ms
(- (fabs (- m n)) (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) l))

series327.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
215.0ms
(- (fabs (- m n)) (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) l))
112.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify8.5s

Counts
63 → 72
Calls
63 calls:
Slowest
398.0ms
(/ (exp (fabs (- m n))) (* (exp (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) (exp l)))
390.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (/ (+ m n) 2) M))
384.0ms
(/ (exp (fabs (- m n))) (exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) l)))
380.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
373.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize89.0ms

Local error

Found 4 expressions with local error:

35.6b
(cos (- (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2)) M))
1.0b
(cbrt 2)
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 47
Calls
4 calls:
Slowest
65.0ms
(cos (- (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2)) M))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series283.0ms

Counts
4 → 6
Calls
4 calls:
Slowest
283.0ms
(cos (- (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2)) M))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify918.0ms

Counts
18 → 53
Calls
18 calls:
Slowest
209.0ms
(* (cos (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2))) (cos (- M)))
201.0ms
(* (cos (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2))) (cos (- M)))
191.0ms
(* (cos (/ (/ (* (+ m n) K) (* (cbrt 2) (cbrt 2))) (cbrt 2))) (cos M))
136.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
114.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune989.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes545.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch2.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.7s8098×body80valid
192.0ms147×body1280valid
156.0ms164×body640valid
62.0ms87×body320valid
58.0ms59×body160valid
8.0ms4×body2560valid