Details

sample3.3m (37.6%)

Algorithm
61×intervals
Results
41.0s253181×body80valid
38.7s29050×body1280valid
26.3s159688×body80nan
20.0s20399×body640valid
19.3s8830×body2560valid
11.0s3436×body5120valid
6.0s9922×body320valid
2.8s9089×body160valid
1.2s662×body10240exit
781.0ms627×body640nan
313.0ms621×body1280nan
177.0ms8256×pre80true
141.0ms166×body160nan
112.0ms376×body320nan

series2.6m (29.8%)

Calls

436 calls:

7.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune1.4m (16.4%)

rewrite44.1s (8.5%)

Algorithm
114×rewrite-expression-head
Calls

436 calls:

2.4s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(* (/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(log (exp (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x)))))))
Rules
36814×add-exp-log
26116×prod-exp
14999×pow-exp
11067×div-exp
6540×pow-to-exp
6238×times-frac
5134×add-sqr-sqrt
4865×sqrt-prod
4725×*-un-lft-identity
4165×add-cube-cbrt
2546×add-cbrt-cube
1817×rec-exp 1-exp
1397×associate-*l*
1394×pow1
1324×sqrt-div
1267×cbrt-prod
1088×associate-*r*
1071×frac-times
1023×cbrt-unprod
749×associate-*r/
697×unpow-prod-down
613×flip3-- flip--
539×add-log-exp
525×associate-*l/
447×pow-prod-down
445×cbrt-undiv
386×pow-unpow
363×associate-/l*
319×unswap-sqr
298×associate-/r*
273×div-inv
191×sqr-pow
171×flip-+ flip3-+
170×sqrt-pow1
153×distribute-lft-out
150×distribute-lft-out--
144×*-commutative
139×associate-/r/
119×cbrt-div
114×exp-prod
113×difference-of-squares
94×pow1/3
89×clear-num frac-2neg
79×pow1/2 distribute-rgt-neg-in
78×distribute-rgt-in distribute-lft-in
76×tan-quot
69×pow-prod-up
67×sub-neg
62×distribute-lft-neg-in log-pow
57×cube-prod
54×pow-pow
53×rem-sqrt-square
50×unpow2
47×pow-sqr
46×swap-sqr
44×frac-sub
35×div-sub
34×sum-log log-prod
27×pow-sub
26×pow-plus pow-flip
24×+-commutative associate--l+
23×associate-/l/
21×diff-log pow2
20×frac-add
11×unpow3 cube-mult
10×neg-sub0 exp-sum
9×rem-cube-cbrt associate-+r+
8×neg-mul-1 associate--r+
7×rem-log-exp
6×cos-sum inv-pow neg-log
5×associate-+l+ acos-asin
4×pow-div pow-neg distribute-neg-frac
3×exp-diff associate--l- cos-diff unpow-prod-up sum-cubes
2×cube-div un-div-inv rem-exp-log sqrt-unprod rem-square-sqrt distribute-frac-neg asin-acos associate--r- rem-cbrt-cube associate-+l- log-div
1×sqrt-undiv e-exp-1 associate-+r- exp-neg unsub-neg mul0 exp-to-pow

simplify15.5s (3.0%)

regimes14.2s (2.7%)

Accuracy

Total 47.3b remaining (21.6%)

Threshold costs 5.8b (2.6%)

8.8b-11.6%Henrywood and Agarwal, Equation (12)
8.2b16.4%Toniolo and Linder, Equation (13)
7.6b6.8%Toniolo and Linder, Equation (10+)
5.2b78%Toniolo and Linder, Equation (7)
3.5b-74%Henrywood and Agarwal, Equation (9a)

bsearch5.8s (1.1%)

localize4.6s (0.9%)

end2.0ms (0.0%)