Details

simplify7.2m (44.2%)

sample3.2m (19.8%)

Algorithm
61×intervals
Results
43.2s252181×body80valid
40.3s29453×body1280valid
27.7s160173×body80nan
20.3s8772×body2560valid
19.2s20296×body640valid
10.8s3360×body5120valid
6.2s9995×body320valid
3.2s9078×body160valid
1.1s644×body10240exit
765.0ms670×body640nan
292.0ms623×body1280nan
226.0ms8256×pre80true
174.0ms176×body160nan
147.0ms340×body320nan

series2.6m (16.1%)

Calls

445 calls:

7.4s
(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*))))))
7.2s
(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*)))))
7.2s
(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*)))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.0s
(* (* (* 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*)))))

prune2.0m (12.0%)

rewrite39.3s (4.0%)

Algorithm
114×rewrite-expression-head
Calls

445 calls:

3.1s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.6s
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
1.2s
(- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k)))
1.2s
(* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))))
Rules
20372×add-exp-log
13585×prod-exp
5189×div-exp
4653×pow-exp
3856×add-sqr-sqrt
3624×times-frac
3487×*-un-lft-identity
2930×add-cube-cbrt
2799×add-cbrt-cube
2230×sqrt-prod
2228×pow-to-exp
1309×associate-*l*
1301×pow1
1228×cbrt-unprod
869×associate-*l/
783×associate-*r/
773×frac-times
749×associate-*r*
725×sqrt-div
679×unpow-prod-down
613×1-exp rec-exp
565×cbrt-undiv
555×add-log-exp
427×pow-prod-down
371×frac-add
365×flip-+ flip3-+
339×pow-unpow
332×associate-/l*
316×cbrt-prod
298×flip3-- flip--
278×associate-/r*
263×unswap-sqr
226×div-inv
216×frac-sub
198×sqr-pow
185×distribute-lft-out
178×cbrt-div
149×*-commutative
145×sqrt-pow1
141×difference-of-squares
125×associate-/r/
124×distribute-lft-out--
113×pow1/2
109×tan-quot
98×rem-sqrt-square
86×frac-2neg clear-num
75×sub-neg
71×distribute-rgt-in distribute-lft-in
61×swap-sqr
54×pow1/3
49×associate-/l/
45×distribute-rgt-neg-in distribute-lft-neg-in
40×pow-pow
34×associate--l+
31×diff-log
30×div-sub
27×sum-log
26×pow-sub
25×+-commutative
23×pow-prod-up
21×sub-div
20×exp-prod
13×exp-sum pow-sqr
12×neg-sub0 associate--r+ pow-neg
pow-plus neg-mul-1
unpow-prod-up
pow-flip pow2 inv-pow rem-exp-log
log-pow un-div-inv
associate--l- log-prod associate-+r- associate-+r+ distribute-frac-neg asin-acos acos-asin
sqrt-unprod
associate-+l+ exp-diff cos-sum rem-square-sqrt e-exp-1
sqrt-undiv distribute-rgt-neg-out cos-diff rem-log-exp

regimes26.6s (2.7%)

Accuracy

Total 56.5b remaining (24.4%)

Threshold costs 4.1b (1.8%)

10.8b11.2%Toniolo and Linder, Equation (13)
8.1b13.9%Maksimov and Kolovsky, Equation (3)
7.9b45.1%Henrywood and Agarwal, Equation (3)
6.8b0%Henrywood and Agarwal, Equation (12)
5.6b76.4%Toniolo and Linder, Equation (7)

localize8.3s (0.8%)

bsearch3.0s (0.3%)

end0.0ms (0.0%)