Details

sample2.0m (37.3%)

Algorithm
61×intervals
Results
32.0s253394×body80valid
21.4s161512×body80nan
19.5s29632×body1280valid
10.7s8938×body2560valid
9.4s20393×body640valid
6.4s3339×body5120valid
3.2s9835×body320valid
2.0s9174×body160valid
756.0ms794×body10240exit
269.0ms628×body1280nan
223.0ms639×body640nan
174.0ms8256×pre80true
97.0ms351×body320nan
33.0ms167×body160nan

series1.7m (30.9%)

Calls

447 calls:

4.8s
(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*)))))
4.6s
(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*))))))
4.5s
(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*))))

prune1.0m (18.9%)

rewrite13.3s (4.1%)

Algorithm
117×rewrite-expression-head
Calls

447 calls:

878.0ms
(* (cbrt (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))) (cbrt (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
678.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
660.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
461.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
428.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (* PI (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))) (sqrt (+ (* 1.0 1.0) (+ (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
Rules
29925×add-exp-log
21055×prod-exp
11090×pow-exp
8510×div-exp
5182×add-sqr-sqrt
4892×pow-to-exp
4718×*-un-lft-identity
4653×times-frac
3766×add-cube-cbrt
2659×add-cbrt-cube
1848×sqrt-prod
1357×pow1
1311×1-exp rec-exp
1079×unpow-prod-down
1021×cbrt-unprod
1016×associate-*r*
858×associate-*l*
797×prod-diff
780×cbrt-prod
540×cbrt-undiv
536×add-log-exp
472×associate-/l*
447×log1p-expm1-u expm1-log1p-u
436×pow-prod-down
420×associate-/r*
398×difference-of-squares
391×sqr-pow
353×associate-*r/
327×div-inv
325×distribute-lft-out--
304×pow-unpow
299×unswap-sqr
233×distribute-lft-out
232×sqrt-div
203×distribute-rgt-neg-in
187×distribute-lft-neg-in
181×distribute-rgt-in distribute-lft-in
162×flip3-- flip--
153×*-commutative
151×cube-prod
148×associate-/r/
112×clear-num frac-2neg
107×fma-neg
94×flip-+ flip3-+
82×fma-def
73×sqrt-pow1
69×frac-times
67×associate-*l/
65×sub-neg
52×pow1/2 pow-prod-up
51×rem-sqrt-square pow-pow
50×associate-/l/
48×unpow2
46×swap-sqr
42×associate--l+
41×cbrt-div
38×pow-sqr
35×pow1/3
33×frac-sub
32×unpow3 cube-mult
25×cos-sum fma-udef pow-plus sum-log tan-quot
24×div-sub
23×+-commutative
22×diff-log associate--r+
20×pow2
19×neg-mul-1
17×pow-sub
16×un-div-inv
15×hypot-def
14×difference-cubes log-pow
13×exp-prod
12×pow-neg hypot-udef neg-sub0
11×pow-flip
10×frac-add associate-+r+
8×inv-pow exp-neg asin-acos distribute-rgt-neg-out
5×unpow-prod-up
4×mul-1-neg neg-log associate--r- log-rec
3×sqrt-undiv sqrt-pow2 sqrt-unprod log-prod
2×cube-div rem-cube-cbrt associate--l- associate-+l+ distribute-neg-frac
1×cos-diff unsub-neg rem-square-sqrt distribute-frac-neg associate-+r- acos-asin mul0 rem-cbrt-cube rem-log-exp

simplify12.2s (3.8%)

Algorithm
177×egg-herbie

regimes10.7s (3.3%)

Accuracy

Total 40.0b remaining (19.5%)

Threshold costs 3.8b (1.9%)

8.2b11.7%Toniolo and Linder, Equation (13)
5.9b57.5%Henrywood and Agarwal, Equation (3)
5.8b75.4%Toniolo and Linder, Equation (7)
5.0b0%Henrywood and Agarwal, Equation (12)
3.0b46.7%Toniolo and Linder, Equation (10+)

bsearch2.9s (0.9%)

localize2.4s (0.8%)

end1.0ms (0.0%)