Details

simplify6.1m (42.0%)

sample3.4m (23.4%)

Algorithm
61×intervals
Results
44.5s253418×body80valid
40.3s29403×body1280valid
29.1s160336×body80nan
20.4s20091×body640valid
18.2s8852×body2560valid
10.0s3375×body5120valid
7.7s10024×body320valid
3.4s8958×body160valid
856.0ms669×body10240exit
477.0ms8256×pre80true
385.0ms611×body640nan
385.0ms592×body1280nan
198.0ms352×body320nan
89.0ms188×body160nan

series2.5m (17.1%)

Calls

448 calls:

8.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.4m (9.7%)

rewrite45.3s (5.2%)

Algorithm
118×rewrite-expression-head
Calls

448 calls:

1.6s
(* (* (* (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))
1.4s
(* (* (* (/ (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))
1.3s
(+ (/ c0 (/ (* (* w h) (* D D)) (* d d))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
916.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
Rules
56266×add-exp-log
41584×prod-exp
28818×pow-exp
19809×div-exp
12800×pow-to-exp
7647×times-frac
6048×add-sqr-sqrt
5413×*-un-lft-identity
4821×1-exp
4792×rec-exp
4575×add-cube-cbrt
2570×add-cbrt-cube
2397×sqrt-prod
1578×unpow-prod-down
1340×pow1
1063×cbrt-unprod
1031×associate-*r*
998×associate-*l*
558×add-log-exp
510×sqr-pow
499×associate-*r/
486×pow-unpow
481×cbrt-undiv
477×associate-/l*
436×unswap-sqr
428×associate-/r*
419×pow-prod-down
371×cbrt-prod
329×div-inv
328×associate-*l/
318×sqrt-div
282×frac-times
250×distribute-lft-out
237×difference-of-squares
228×flip-+ flip3-+
225×exp-prod
215×distribute-lft-out--
190×flip3-- flip--
187×associate-/r/
153×*-commutative
121×cbrt-div
118×sqrt-pow1
107×tan-quot
104×unpow2
89×frac-2neg clear-num
81×pow1/2
76×distribute-rgt-in distribute-lft-in
66×pow1/3
62×rem-sqrt-square
61×sub-neg
57×pow-pow
56×pow-prod-up
47×associate-/l/
42×cube-div
40×sum-log swap-sqr
36×pow-sqr
35×div-sub
32×frac-sub
28×+-commutative distribute-rgt-neg-in
26×distribute-lft-neg-in associate--l+
24×log-prod
23×pow-plus
20×frac-add log-pow
18×pow2
17×cube-prod
15×pow-sub
12×diff-log rem-cube-cbrt
11×rem-exp-log
10×associate-+r+ neg-sub0
9×exp-diff pow-flip
8×unpow3 cube-mult pow-neg associate-+r-
7×inv-pow
6×cos-sum acos-asin rem-log-exp
5×exp-sum
4×distribute-neg-frac neg-log asin-acos associate-+l-
3×cos-diff exp-to-pow
2×un-div-inv associate--l- sqrt-unprod associate-+l+ rem-square-sqrt neg-mul-1 associate--r+ log-div
1×mul0 exp-lft-cube rem-cbrt-cube

regimes15.3s (1.8%)

Accuracy

Total 42.7b remaining (20.2%)

Threshold costs 4.8b (2.3%)

9.3b25.7%Toniolo and Linder, Equation (13)
5.8b75.7%Toniolo and Linder, Equation (7)
5.6b4%Henrywood and Agarwal, Equation (12)
4.8b32.8%Toniolo and Linder, Equation (10+)
4.6b-47.3%Henrywood and Agarwal, Equation (13)

localize4.8s (0.6%)

bsearch3.3s (0.4%)

end0.0ms (0.0%)