Details

series1.7m (30.4%)

Calls

466 calls:

5.0s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
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*))))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.5m (26.1%)

sample1.4m (24.6%)

Algorithm
61×intervals
Results
15.0s28894×body1280valid
14.8s253029×body80valid
9.3s161881×body80nan
8.7s8880×body2560valid
6.9s20339×body640valid
5.4s3349×body5120valid
2.3s9946×body320valid
1.2s9146×body160valid
535.0ms976×body10240exit
139.0ms619×body1280nan
110.0ms652×body640nan
96.0ms8256×pre80true
44.0ms348×body320nan
18.0ms194×body160nan

rewrite34.0s (10.1%)

Algorithm
119×rewrite-expression-head
Calls

466 calls:

1.7s
(* (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))) (sqrt (* (* (* (/ (sqrt 2.0) 4.0) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))
1.6s
(* (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))) (sqrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))))
1.1s
(* (* (* (/ (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))
936.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
932.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
42669×add-exp-log
30181×prod-exp
21861×sqrt-div
18379×pow-exp
13908×div-exp
11951×frac-times
8719×pow-to-exp
6582×times-frac
6072×flip3-- flip--
5295×add-sqr-sqrt
5288×*-un-lft-identity
4748×associate-*l/
4256×add-cube-cbrt
3361×associate-*r/
2807×add-cbrt-cube
2071×1-exp rec-exp
1973×sqrt-prod
1744×unpow-prod-down
1576×pow1
1300×associate-*l*
1165×cbrt-unprod
983×associate-*r*
677×cbrt-prod
598×add-log-exp
568×cbrt-undiv
550×pow-prod-down
461×sqr-pow
420×pow-unpow
364×associate-/r* unswap-sqr
339×associate-/l*
324×distribute-lft-out
303×div-inv
293×distribute-lft-out--
251×flip-+ flip3-+
209×associate-/r/
206×sqrt-pow1
193×distribute-rgt-neg-in
163×*-commutative
160×difference-of-squares
140×distribute-lft-neg-in
118×exp-prod
92×distribute-rgt-in distribute-lft-in
89×cbrt-div
88×pow1/2
87×frac-2neg clear-num
81×pow-prod-up
77×sub-neg
71×unpow2 pow1/3
66×rem-sqrt-square
55×tan-quot
54×pow-sqr
51×associate-/l/ div-sub
49×swap-sqr
47×frac-sub
46×pow-pow
44×sum-log
34×+-commutative
32×associate--l+
28×pow-plus
27×diff-log
26×pow-sub
22×frac-add pow2
20×neg-mul-1
16×neg-sub0
14×associate-+r+
12×log-prod
11×cube-prod
9×log-pow log-div
8×distribute-neg-frac associate--r+
7×inv-pow pow-flip associate-+l-
6×cos-sum associate-+r- neg-log
5×un-div-inv distribute-frac-neg
4×pow-neg unsub-neg acos-asin asin-acos
3×unpow3 associate-+l+ distribute-rgt-out-- cos-diff cube-mult
2×cube-div exp-diff rem-exp-log associate--l- sqrt-unprod exp-neg rem-square-sqrt associate--r- rem-log-exp
1×sqrt-undiv distribute-lft-neg-out sub-div mul0 rem-cbrt-cube

simplify14.5s (4.3%)

Algorithm
179×egg-herbie

regimes11.2s (3.3%)

Accuracy

Total 50.5b remaining (22.9%)

Threshold costs 4.7b (2.1%)

10.1b21.2%Toniolo and Linder, Equation (13)
9.3b31.6%Henrywood and Agarwal, Equation (3)
5.5b76.8%Toniolo and Linder, Equation (7)
4.7b-3.9%Henrywood and Agarwal, Equation (12)
4.2b48%Toniolo and Linder, Equation (10+)

localize2.3s (0.7%)

bsearch1.5s (0.5%)

end1.0ms (0.0%)