Details

simplify22.0m (60.8%)

prune7.9m (21.8%)

sample4.0m (11.1%)

Algorithm
60×intervals
Results
58.3s247976×body80valid
50.0s27173×body1280valid
37.6s159936×body80nan
25.1s18834×body640valid
22.5s8764×body2560valid
13.9s3377×body5120valid
8.9s9217×body320valid
4.8s8373×body160valid
1.5s648×body10240exit
571.0ms632×body1280nan
496.0ms628×body640nan
320.0ms8256×pre80true
181.0ms360×body320nan
64.0ms193×body160nan

series1.4m (3.8%)

Calls

435 calls:

2.2s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (* (- U* U) (* (/ (* (cbrt l) (cbrt n)) (cbrt Om)) (/ (* (cbrt l) (cbrt n)) (cbrt Om)))) (/ (cbrt l) (/ (cbrt Om) (cbrt n)))))))))))
2.2s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
2.1s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))
2.1s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))
2.1s
(sqrt (* U (* n (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n))))))))))

rewrite26.6s (1.2%)

Algorithm
112×rewrite-expression-head
Calls

435 calls:

1.2s
(* (/ (* (/ (cbrt 2) (cbrt (sin k))) (/ (cbrt 2) (cbrt (sin k)))) (* (+ (* (/ k t) (/ k t)) 2) (/ (cbrt t) (/ (/ l t) (cbrt t))))) (/ (/ (/ (cbrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t))) (tan k)))
867.0ms
(* E (exp (exp (/ (+ (+ (- mu Ec) EDonor) Vef) KbT))))
492.0ms
(+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)
410.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2) M))
362.0ms
(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
Rules
107594×times-frac
43852×add-sqr-sqrt
43317×*-un-lft-identity
42241×add-cube-cbrt
19084×cbrt-prod
11465×associate-*r*
10539×sqrt-prod
9394×add-exp-log
8347×frac-times
7693×associate-/r/
7434×add-cbrt-cube
5583×associate-*r/
5419×associate-*l/
4264×div-exp
4034×div-inv
3781×cbrt-undiv
3160×prod-exp
2851×cbrt-unprod
1819×associate-/l*
1570×pow1
1337×associate-*l*
837×difference-of-squares
695×associate-/r*
549×add-log-exp
500×unpow-prod-down
479×sqrt-div
435×insert-posit16
415×flip-+ flip3-+
410×pow-prod-down
322×unswap-sqr
251×distribute-lft-out
249×flip3-- flip--
179×swap-sqr
168×sqrt-pow1 frac-add
155×*-commutative
144×sqr-pow
130×distribute-lft-out--
121×cbrt-div
120×1-exp
115×pow1/2
113×pow-prod-up
97×frac-2neg clear-num
94×rem-sqrt-square
88×distribute-rgt-in distribute-lft-in
79×pow-unpow
78×log-pow
74×pow-plus
69×pow-exp associate-/l/
59×sin-mult
54×sum-log
49×sub-neg
48×pow-to-exp
47×exp-prod
44×pow-sqr
42×pow1/3
40×rec-exp
37×pow2
27×pow-pow
26×unpow-prod-up
25×+-commutative div-sub
23×tan-quot
21×distribute-rgt-out
17×log-prod
15×pow-flip distribute-lft1-in
14×frac-sub
12×diff-log
11×exp-to-pow
10×cube-prod pow-sub distribute-rgt1-in
associate-+r+ inv-pow acos-asin
pow3
cube-unmult sqr-sin
associate-+l+ exp-sum cos-sum cube-div
rem-exp-log count-2
un-div-inv rem-log-exp log-div
associate-+r- distribute-rgt-out-- cos-diff
exp-diff associate--l+ unpow2 asin-acos associate-+l- rem-cbrt-cube
remove-posit16 unpow3 sqrt-unprod sub-div sqrt-pow2 rem-square-sqrt cube-mult e-exp-1

regimes17.0s (0.8%)

Accuracy

Total 44.8b remaining (22%)

Threshold costs 4.1b (2%)

8.6b23.5%Toniolo and Linder, Equation (13)
8.3b2%Maksimov and Kolovsky, Equation (3)
5.1b10.2%Henrywood and Agarwal, Equation (12)
5.1b78.1%Toniolo and Linder, Equation (7)
3.5b0%Given's Rotation SVD example

localize6.3s (0.3%)

bsearch4.5s (0.2%)

end1.0ms (0.0%)