Details

simplify16.6m (49.3%)

prune7.1m (21.1%)

sample4.3m (12.7%)

Algorithm
61×intervals
Results
1.0m252730×body80valid
51.3s29117×body1280valid
38.9s160656×body80nan
27.0s20337×body640valid
22.5s8721×body2560valid
13.2s3435×body5120valid
8.0s9966×body320valid
4.0s9018×body160valid
1.4s745×body10240exit
1.1s8256×pre80true
919.0ms670×body640nan
397.0ms602×body1280nan
127.0ms344×body320nan
109.0ms204×body160nan

series3.7m (10.9%)

Calls

430 calls:

10.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) 2.0)) (* (cbrt (- U U*)) (cbrt (- U U*)))) (cbrt (- U U*))))))
10.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
10.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite1.1m (3.1%)

Algorithm
113×rewrite-expression-head
Calls

430 calls:

4.1s
(* (cos (- (* (/ K 2.0) (+ n m)) M)) (exp (- (- (fabs (- m n)) l) (pow (- (/ (+ n m) 2.0) M) 2.0))))
3.1s
(/ (+ 0 (* M M)) (- (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h) (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h) (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h)) (* M M)))))
1.8s
(cos (- (* (* (/ K 2.0) (* (* (cbrt (- n)) (cbrt -1)) (cbrt (+ n m)))) (cbrt (+ n m))) M))
1.6s
(cbrt (* (* (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
1.6s
(+ (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h) (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h) (/ (* (* (/ d D) (/ d D)) (/ c0 w)) h)) (* M M))))
Rules
68761×times-frac
42212×add-exp-log
25714×add-sqr-sqrt
25263×*-un-lft-identity
25028×prod-exp
24940×add-cube-cbrt
17044×unpow-prod-down
16026×div-exp
14027×pow-exp
4562×pow-to-exp
4199×div-inv
2988×sqr-pow
2880×add-cbrt-cube
2340×1-exp rec-exp
2177×associate-/r/
1890×pow1
1766×tan-quot
1600×sqrt-prod
1130×associate-/l*
1110×cbrt-unprod
1030×sqrt-pow1
833×associate-*r*
738×associate-*l*
694×cbrt-undiv
677×associate-*r/
540×pow-prod-down
531×add-log-exp
528×pow1/2
514×pow-prod-up
437×associate-/r*
433×flip3-- flip--
423×cbrt-div
418×cbrt-prod
375×sqrt-div
359×frac-times
322×associate-*l/
240×unswap-sqr
237×pow-unpow
222×pow-sqr
196×frac-sub
177×flip-+ flip3-+
145×*-commutative
122×difference-of-squares
110×distribute-lft-out
103×pow1/3
82×clear-num frac-2neg
77×distribute-rgt-in distribute-lft-in
76×sub-neg
72×rem-sqrt-square
65×distribute-lft-out--
45×pow-plus swap-sqr
41×associate-/l/
35×pow2
32×pow-pow
31×sum-log
30×associate--l+
26×frac-add
24×diff-log
21×+-commutative
19×div-sub
15×pow-sub
12×distribute-lft-neg-in distribute-rgt-neg-in
11×sqrt-unprod
10×pow-flip exp-sum
9×associate-+l+
8×cos-sum inv-pow associate-+r+
7×un-div-inv
6×exp-prod log-prod
4×associate-+r- sub-div cube-prod neg-mul-1
3×exp-diff sqrt-undiv cos-diff distribute-rgt-out-- log-pow rem-square-sqrt distribute-frac-neg neg-sub0 pow-neg unpow2
2×associate--l- acos-asin asin-acos log-div
1×rem-exp-log pow3 sum-cubes rem-cbrt-cube associate-+l-

regimes37.4s (1.8%)

Accuracy

Total 58.1b remaining (28.4%)

Threshold costs 4.8b (2.3%)

9.2b11.5%Henrywood and Agarwal, Equation (13)
8.8b10.6%Toniolo and Linder, Equation (13)
8.0b10.4%Maksimov and Kolovsky, Equation (3)
6.8b-5.2%Henrywood and Agarwal, Equation (12)
6.1b22.3%Toniolo and Linder, Equation (10-)

localize12.0s (0.6%)

bsearch8.3s (0.4%)

end1.0ms (0.0%)