Details

prune1.9m (30.7%)

sample1.8m (30.3%)

Algorithm
59×intervals
Results
26.8s243643×body80valid
20.1s29722×body1280valid
17.4s158040×body80nan
10.5s8775×body2560valid
9.6s20148×body640valid
6.2s3347×body5120valid
3.2s9703×body320valid
2.2s9056×body160valid
615.0ms606×body10240exit
276.0ms606×body1280nan
218.0ms588×body640nan
149.0ms8256×pre80true
98.0ms359×body320nan
34.0ms185×body160nan
18.0ms231×body80overflowed

series1.5m (24.6%)

Calls

437 calls:

4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(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*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.6s
(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*))))))
1.5s
(* (* (* 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*))))

rewrite22.8s (6.2%)

Algorithm
114×rewrite-expression-head
Calls

437 calls:

1.7s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
991.0ms
(/ (/ (/ NaChar (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))) (sqrt (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))) (sqrt (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
801.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
560.0ms
(/ (/ NaChar (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))) (sqrt (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
558.0ms
(/ (/ NaChar (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))) (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
Rules
43454×times-frac
37067×add-exp-log
24248×prod-exp
22093×*-un-lft-identity
20434×add-sqr-sqrt
19101×add-cube-cbrt
14337×pow-exp
13712×div-exp
12631×sqrt-prod
8541×unpow-prod-down
7022×pow-to-exp
4419×cbrt-prod
4235×associate-*r*
2259×add-cbrt-cube
1702×1-exp rec-exp
1573×sqr-pow
1482×pow1
1225×distribute-lft-out
1184×associate-/l*
1067×associate-*l*
847×cbrt-unprod
752×div-inv
731×unpow2
608×sqrt-div
563×add-log-exp
456×pow-unpow
433×associate-/r/
430×associate-*r/
428×associate-/r*
419×pow-prod-down
416×unswap-sqr
394×cbrt-undiv
375×distribute-lft-out--
322×flip-+ flip3-+
305×exp-prod
235×distribute-rgt-neg-in
207×distribute-lft-neg-in
188×associate-*l/
156×flip3-- flip--
144×*-commutative
138×difference-of-squares
136×frac-times
115×pow-prod-up
100×clear-num frac-2neg
97×sqrt-pow1
93×log-pow
85×cube-prod
83×distribute-rgt-in distribute-lft-in
76×sub-neg
72×pow1/2
71×pow-sqr
70×pow-pow
60×tan-quot
57×frac-sub
56×associate-/l/ pow-plus
55×rem-sqrt-square
54×swap-sqr
43×log-prod
42×pow2
40×div-sub
39×sum-log
30×pow1/3
27×diff-log neg-mul-1
26×+-commutative
24×associate--l+
23×cbrt-div
22×neg-sub0
20×frac-add pow-flip
18×pow-sub
17×associate-+r+
15×unpow3 cube-mult
14×pow-neg
10×cos-sum
8×inv-pow rem-log-exp log-div
7×rem-cube-cbrt distribute-rgt-out-- sub-div distribute-frac-neg
6×exp-diff distribute-neg-frac
5×un-div-inv rem-exp-log cos-diff neg-log
4×pow-div cube-div associate-+r- exp-neg distribute-neg-in unsub-neg acos-asin exp-sum associate--r+
3×associate-+l+ asin-acos rem-cbrt-cube
2×sqrt-pow2 associate--l- associate--r-
1×sqrt-undiv sqrt-unprod rem-square-sqrt mul0

simplify15.2s (4.2%)

Algorithm
172×egg-herbie

regimes10.3s (2.8%)

Accuracy

Total 42.6b remaining (19.9%)

Threshold costs 5.4b (2.5%)

8.0b38.2%Henrywood and Agarwal, Equation (3)
7.3b25.8%Toniolo and Linder, Equation (13)
5.4b76.9%Toniolo and Linder, Equation (7)
5.3b13.7%Henrywood and Agarwal, Equation (12)
3.3b57%Toniolo and Linder, Equation (10+)

localize2.2s (0.6%)

bsearch2.0s (0.5%)

end1.0ms (0.0%)