Details

series2.0m (40.4%)

Calls

431 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*)))))
4.8s
(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 (/ 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*))))))
1.9s
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

sample1.4m (27.9%)

Algorithm
61×intervals
Results
16.0s29598×body1280valid
15.6s253256×body80valid
9.9s162450×body80nan
8.8s8843×body2560valid
7.5s20361×body640valid
5.4s3321×body5120valid
2.3s9998×body320valid
1.5s8975×body160valid
477.0ms816×body10240exit
146.0ms628×body1280nan
119.0ms652×body640nan
108.0ms8256×pre80true
50.0ms372×body320nan
19.0ms192×body160nan

prune55.8s (19.1%)

simplify11.3s (3.9%)

Algorithm
175×egg-herbie

rewrite11.1s (3.8%)

Algorithm
115×rewrite-expression-head
Calls

431 calls:

467.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
465.0ms
(/ 1 (* (cbrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))) (cbrt (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
346.0ms
(* (* (* (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))))
342.0ms
(* (* (* (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
288.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
Rules
32697×add-exp-log
23038×prod-exp
11775×pow-exp
9213×div-exp
5094×pow-to-exp
4289×add-sqr-sqrt
4057×times-frac
3805×*-un-lft-identity
3195×add-cube-cbrt
2549×add-cbrt-cube
1491×1-exp rec-exp
1147×pow1
1063×cbrt-unprod
1032×pow-unpow
940×sqrt-prod
841×associate-*r*
795×unpow-prod-down
727×associate-*r/
701×associate-*l*
637×cbrt-prod
509×sqrt-div
476×cbrt-undiv
475×add-log-exp
431×log1p-expm1-u expm1-log1p-u
356×pow-prod-down
317×flip3-- flip--
305×cbrt-div
283×prod-diff
282×frac-times
280×associate-/l*
274×div-inv
264×associate-/r*
260×unswap-sqr
252×associate-/r/
229×sqr-pow
223×difference-of-squares
185×associate-*l/
179×distribute-lft-out--
167×distribute-rgt-in distribute-lft-in
155×distribute-rgt-neg-in
146×distribute-lft-neg-in
142×distribute-lft-out
140×*-commutative
122×sqrt-pow1
113×flip-+ flip3-+
83×frac-2neg clear-num
80×pow1/2
78×pow1/3
67×rem-sqrt-square
63×pow-pow
61×cube-prod
55×fma-def swap-sqr
54×sub-neg
45×div-sub
42×associate--l+
36×hypot-def
32×frac-sub
31×exp-prod
27×pow-sub
24×unpow2
23×associate-/l/ cos-sum
20×tan-quot
19×fma-udef pow-prod-up
17×fma-neg sum-log
15×pow-sqr +-commutative neg-sub0
14×pow-neg neg-mul-1
13×pow-flip
10×distribute-frac-neg
7×rem-cube-cbrt un-div-inv pow2
6×unpow3 cube-mult
5×diff-log inv-pow pow-plus
4×cube-div frac-add hypot-udef associate-+r+ acos-asin
3×exp-diff asin-acos rem-cbrt-cube
2×distribute-neg-frac
1×rem-exp-log sqrt-undiv sqrt-pow2 sqrt-unprod associate-+r- cos-diff associate-+l+ expm1-log1p unsub-neg rem-square-sqrt mul0 distribute-rgt-neg-out expm1-udef

regimes10.7s (3.7%)

Accuracy

Total 43.1b remaining (21.2%)

Threshold costs 4.2b (2%)

9.6b34.6%Henrywood and Agarwal, Equation (3)
8.3b8.2%Toniolo and Linder, Equation (13)
5.6b0%Henrywood and Agarwal, Equation (12)
5.6b76.5%Toniolo and Linder, Equation (7)
4.1b43.2%Toniolo and Linder, Equation (10-)

localize2.2s (0.8%)

bsearch1.6s (0.5%)

end1.0ms (0.0%)