Details

simplify19.7m (67.0%)

sample4.0m (13.6%)

Algorithm
60×intervals
Results
58.4s246712×body80valid
47.1s26816×body1280valid
36.7s160368×body80nan
26.2s18859×body640valid
22.6s8763×body2560valid
14.6s3433×body5120valid
9.6s9259×body320valid
4.5s8689×body160valid
1.5s640×body10240exit
644.0ms638×body1280nan
567.0ms631×body640nan
358.0ms8256×pre80true
244.0ms356×body320nan
71.0ms199×body160nan

prune3.4m (11.5%)

series1.3m (4.5%)

Calls

438 calls:

3.5s
(sqrt (+ (* U (* (* t 2) n)) (* (/ n (/ Om l)) (* (- (- (* l 2) (* (- U* U) (/ n (/ Om l))))) (* 2 U)))))
3.1s
(sqrt (+ (* U (* (* t 2) n)) (* (* (/ n (/ Om l)) (- (- (* l 2) (* (- U* U) (/ n (/ Om l)))))) (* 2 U))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.0s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite32.8s (1.9%)

Algorithm
113×rewrite-expression-head
Calls

438 calls:

1.3s
(/ (- (pow 1 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)) (+ (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))))
946.0ms
(* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
939.0ms
(* J (* (cos (/ K 2)) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l))))))
929.0ms
(* (+ (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (+ (/ 1/2 (hypot 1 x)) 1/2) 1)) (* (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1)))
718.0ms
(* (* J (cos (/ K 2))) (+ (* 1/60 (* (* (* l l) (* l l)) l)) (+ (* 2 l) (* 1/3 (* (* l l) l)))))
Rules
264708×times-frac
75190×*-un-lft-identity
75019×add-sqr-sqrt
73816×add-cube-cbrt
46340×cbrt-prod
11596×add-exp-log
10966×div-inv
9386×sqrt-prod
8147×associate-/r/
7048×add-cbrt-cube
6573×frac-times
5510×div-exp
3989×prod-exp
3639×associate-/r*
3565×flip-+ flip3-+
3458×associate-*l/
3451×cbrt-undiv
3421×associate-*r/
2861×frac-add
2743×sqrt-div
2583×cbrt-unprod
1524×pow1
1426×associate-*r*
1363×associate-*l*
1251×associate-/l*
573×add-log-exp
494×unpow-prod-down
490×distribute-lft-out
438×insert-posit16
420×difference-of-squares
399×pow-prod-down
343×1-exp
312×unswap-sqr
270×sqr-pow
249×distribute-lft-out--
220×rec-exp
218×unpow-prod-up
202×exp-prod
180×flip3-- flip--
153×*-commutative
149×sub-neg
133×swap-sqr
128×pow-prod-up
118×distribute-rgt-in distribute-lft-in
112×sqrt-pow1
111×frac-2neg clear-num
106×pow-unpow
98×pow-exp
95×associate-/l/
91×pow1/2
88×log-prod
79×rem-sqrt-square
72×pow-plus
70×exp-sum distribute-neg-in
69×pow-to-exp
67×pow-sqr
59×sum-log
49×pow1/3
47×pow2
46×sin-mult
35×cbrt-div
31×cube-prod log-pow
30×pow-pow
25×+-commutative
23×tan-quot
22×div-sub
21×pow-flip
16×associate-+l+
15×inv-pow diff-log
14×cube-div
11×associate-+r+
10×cos-sum
9×associate-+r- pow-sub
8×pow3
7×cube-mult
5×difference-cubes rem-exp-log cos-diff
4×exp-diff frac-sub exp-neg difference-of-sqr-1 sqr-sin exp-to-pow distribute-neg-frac asin-acos rem-log-exp
3×distribute-lft-neg-out cube-unmult distribute-rgt-neg-out
2×rem-cube-cbrt unpow3 associate--r+ un-div-inv associate--l+ unpow1/3 rem-cbrt-cube
1×sub-div sqrt-pow2 unpow2 acos-asin

regimes18.4s (1.0%)

Accuracy

Total 41.7b remaining (22.5%)

Threshold costs 5.1b (2.7%)

11.2b20.5%Toniolo and Linder, Equation (13)
7.1b17.2%Maksimov and Kolovsky, Equation (3)
5.1b4.8%Henrywood and Agarwal, Equation (13)
5.0b78.3%Toniolo and Linder, Equation (7)
2.8b15.5%Henrywood and Agarwal, Equation (12)

localize6.7s (0.4%)

bsearch2.0s (0.1%)

end1.0ms (0.0%)