Details

simplify7.6m (39.4%)

prune5.2m (27.1%)

sample4.4m (22.8%)

Algorithm
61×intervals
Results
1.0m253593×body80valid
57.2s29533×body1280valid
42.7s161838×body80nan
27.7s20256×body640valid
22.6s8713×body2560valid
13.7s3393×body5120valid
10.1s9909×body320valid
4.6s8934×body160valid
1.5s683×body10240exit
666.0ms606×body1280nan
525.0ms623×body640nan
328.0ms8256×pre80true
189.0ms344×body320nan
99.0ms207×body160nan

series1.3m (7.0%)

Calls

425 calls:

2.8s
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
2.4s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.1s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

rewrite20.6s (1.8%)

Algorithm
113×rewrite-expression-head
Calls

425 calls:

2.3s
(* (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)) (sqrt (+ (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)) 1)))
1.4s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* c0 (/ (/ (* (/ d D) (/ d D)) h) w)))
1.3s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
729.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1 2)) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (/ (* (* h (* (/ M 2) (/ D d))) (* (/ M 2) (/ D d))) (* 2 l))))
688.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* h (* (/ M 2) (/ D d))) (* (/ M 2) (/ D d))) (* 2 l))))
Rules
11868×times-frac
8780×add-sqr-sqrt
8085×*-un-lft-identity
7835×add-exp-log
7614×add-cube-cbrt
5749×add-cbrt-cube
3438×prod-exp
2945×sqrt-prod
2849×prod-diff
2569×div-exp
2374×cbrt-unprod
1914×pow1
1840×cbrt-undiv
1763×unpow-prod-up
1568×frac-times
1351×associate-*r*
1274×associate-*l*
1269×sqrt-div
1108×associate-*l/
872×associate-*r/
722×div-inv
687×associate-/r*
616×pow-prod-down
579×flip-- flip3--
560×associate-/l*
465×add-log-exp
463×associate-/r/
427×expm1-log1p-u
426×log1p-expm1-u
341×unswap-sqr
299×pow-prod-up
285×pow-exp
259×cbrt-div
227×sqrt-pow1
214×unpow-prod-down
185×cbrt-prod
181×difference-of-squares
180×swap-sqr
174×distribute-rgt-in distribute-lft-in
157×*-commutative
144×1-exp rec-exp
127×pow1/2
125×distribute-lft-out--
110×pow-to-exp
107×pow-unpow
102×distribute-lft-out sqr-pow
94×frac-2neg clear-num
87×pow-sqr
75×associate-/l/ sub-neg
65×pow-plus
64×fma-neg fma-udef
52×pow2 rem-sqrt-square
44×pow1/3
35×tan-quot
33×distribute-lft-neg-in distribute-rgt-neg-in
28×flip-+ flip3-+
27×distribute-rgt-out-- neg-mul-1
25×cube-unmult
22×exp-sum
21×fma-def
19×pow-pow
16×exp-prod frac-add
15×pow-flip pow-sub
14×diff-log
10×un-div-inv cos-sum div-sub
9×inv-pow
7×sqrt-unprod hypot-def log-pow
5×sum-log frac-sub +-commutative rem-square-sqrt acos-asin
4×rem-exp-log
3×expm1-log1p expm1-udef log-prod pow3 hypot-udef
2×exp-diff associate-+r- associate--l+ log1p-expm1 associate--r+ sqr-sin asin-acos rem-cbrt-cube cos-diff sin-mult log1p-udef
1×distribute-lft-neg-out sub-div distribute-neg-frac rem-log-exp

regimes16.6s (1.4%)

Accuracy

Total 44.2b remaining (25.8%)

Threshold costs 5.2b (3%)

8.0b29.9%Toniolo and Linder, Equation (13)
7.0b17.5%Henrywood and Agarwal, Equation (13)
6.5b46.5%Henrywood and Agarwal, Equation (3)
5.3b0%Henrywood and Agarwal, Equation (12)
5.2b77.7%Toniolo and Linder, Equation (7)

localize5.6s (0.5%)

bsearch1.3s (0.1%)

end2.0ms (0.0%)