Details

sample1.9m (36.1%)

Algorithm
61×intervals
Results
27.5s253253×body80valid
20.1s29772×body1280valid
17.4s158809×body80nan
10.8s8841×body2560valid
9.4s20314×body640valid
6.4s3475×body5120valid
3.1s9536×body320valid
2.0s9014×body160valid
601.0ms612×body10240exit
271.0ms599×body1280nan
233.0ms647×body640nan
150.0ms8256×pre80true
100.0ms359×body320nan
37.0ms192×body160nan
3.0ms37×body80overflowed

series1.6m (31.6%)

Calls

430 calls:

4.9s
(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*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(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*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune58.0s (18.7%)

rewrite14.1s (4.5%)

Algorithm
113×rewrite-expression-head
Calls

430 calls:

573.0ms
(* (* (* (/ (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))
441.0ms
(* (* (* (/ (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))
410.0ms
(* (* (* (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))
349.0ms
(/ (* (* (* (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)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
321.0ms
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
Rules
25975×add-exp-log
17265×prod-exp
8111×pow-exp
7112×times-frac
7015×div-exp
6563×add-sqr-sqrt
5727×sqrt-prod
5271×*-un-lft-identity
4536×add-cube-cbrt
3054×pow-to-exp
2593×add-cbrt-cube
2308×associate-*l*
1607×unpow-prod-down
1223×pow1
1055×associate-*r*
1045×cbrt-unprod
976×associate-*r/
816×1-exp rec-exp
699×difference-of-squares
638×sqr-pow
533×add-log-exp
478×cbrt-undiv
468×pow-unpow
438×associate-/l*
405×cube-prod
399×pow-prod-down
389×unswap-sqr
366×cbrt-prod associate-/r*
341×frac-times
309×associate-/r/
304×div-inv
298×flip3-- flip--
276×sqrt-div
271×associate-*l/
233×flip-+ flip3-+
230×frac-add
201×distribute-lft-out--
199×distribute-lft-out
178×sqrt-pow1
158×*-commutative
112×pow1/2
101×distribute-rgt-neg-in
88×frac-2neg clear-num
86×distribute-rgt-in distribute-lft-in
84×tan-quot
80×distribute-lft-neg-in
69×exp-prod sub-neg
61×unpow2
59×rem-sqrt-square
51×pow-pow
49×associate-/l/
48×frac-sub
45×div-sub
44×swap-sqr
42×sum-log
40×log-pow
35×pow-sub
33×pow1/3
32×pow-prod-up
30×+-commutative
26×associate--l+
22×cbrt-div
21×difference-cubes
20×pow-sqr
15×log-prod
14×cos-sum
13×un-div-inv pow-flip associate-+r+
12×neg-sub0
11×diff-log
10×pow-neg
9×cube-div inv-pow
8×exp-diff neg-mul-1
7×rem-cube-cbrt cos-diff
6×unpow3 cube-mult pow-plus asin-acos pow2
5×associate-+l+
4×sqrt-unprod exp-sum rem-log-exp
3×rem-square-sqrt log-div
2×rem-exp-log associate-+r- unsub-neg acos-asin distribute-neg-frac
1×sqrt-undiv distribute-frac-neg associate--r- mul0 exp-to-pow

simplify12.3s (3.9%)

Algorithm
173×egg-herbie

regimes10.3s (3.3%)

Accuracy

Total 43.1b remaining (21.1%)

Threshold costs 5.7b (2.8%)

9.6b-4%Toniolo and Linder, Equation (13)
6.8b6.8%Toniolo and Linder, Equation (10+)
5.8b75.5%Toniolo and Linder, Equation (7)
5.7b-5.2%Henrywood and Agarwal, Equation (12)
4.0b46%Toniolo and Linder, Equation (10-)

bsearch3.4s (1.1%)

localize2.2s (0.7%)

end1.0ms (0.0%)