Details

prune8.4m (45.3%)

sample4.3m (23.3%)

Algorithm
61×intervals
Results
1.0m252624×body80valid
54.7s28799×body1280valid
40.6s160368×body80nan
29.7s20582×body640valid
22.6s8763×body2560valid
14.8s3433×body5120valid
9.5s10107×body320valid
4.9s9126×body160valid
1.8s640×body10240exit
760.0ms638×body1280nan
638.0ms631×body640nan
267.0ms356×body320nan
247.0ms8256×pre80true
95.0ms199×body160nan

simplify3.5m (18.8%)

series1.3m (7.3%)

Calls

438 calls:

2.0s
(* (* (* (sqrt (/ (/ 1 (cbrt h)) (cbrt h))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (* (* 2 n) (* U (- t (fma l (* (/ l Om) 2) (* (* (* (* (cbrt n) (/ l Om)) (* (cbrt n) (/ l Om))) (cbrt n)) (- U U*)))))))

rewrite31.3s (2.8%)

Algorithm
116×rewrite-expression-head
Calls

438 calls:

2.3s
(/ (* (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (sqrt (fma (/ k t) (/ k t) 2))) (sqrt (fma (/ k t) (/ k t) 2))) (/ l t))
1.7s
(* (sqrt (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT))) (sqrt (exp (/ (+ EAccept (+ (- Vef mu) Ev)) KbT))))
1.6s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.6s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.4s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
Rules
38418×times-frac
21640×add-sqr-sqrt
20887×*-un-lft-identity
19372×add-cube-cbrt
11480×sqrt-prod
7185×add-exp-log
5293×prod-diff
5112×add-cbrt-cube
4469×unpow-prod-up
2863×div-exp
2641×prod-exp
2126×associate-*l*
2015×cbrt-undiv
1939×div-inv
1856×cbrt-unprod
1481×pow1
1232×associate-*r*
1200×associate-/l*
732×cbrt-prod
615×associate-/r*
550×pow-prod-down
532×add-log-exp
531×difference-of-squares
501×unswap-sqr
497×sqrt-pow1
480×unpow-prod-down
462×distribute-lft-out
440×log1p-expm1-u
438×expm1-log1p-u insert-posit16
431×exp-prod
338×associate-*r/
270×distribute-lft-out--
229×pow-exp
224×associate-*l/
221×sqrt-div
212×distribute-rgt-in sqr-pow distribute-lft-in
202×1-exp
197×swap-sqr
174×frac-times
172×sub-neg
171×associate-/r/
165×pow1/3 pow-prod-up
136×distribute-rgt-neg-in
134×*-commutative
133×pow-sqr
132×distribute-lft-neg-in
128×pow-unpow
123×fma-neg
115×cos-sum
103×flip3-- frac-2neg rec-exp clear-num flip--
102×tan-quot
95×pow1/2
89×pow-to-exp
72×rem-sqrt-square
71×flip-+ flip3-+
68×associate--l+
66×fma-def
59×unpow2
58×associate-/l/
49×pow-plus
43×cbrt-div
37×pow2
29×diff-log
27×div-sub
26×pow-pow
22×associate--r+
21×sum-log
20×frac-sub fma-udef
18×frac-add
17×associate-+r- associate-+l-
15×exp-diff +-commutative
13×pow-flip
12×neg-mul-1
9×inv-pow pow-sub
7×hypot-def
6×log-pow
5×un-div-inv cos-diff
4×associate--l- neg-log difference-of-sqr-1 asin-acos
3×log-prod associate-+r+ pow3 sqrt-unprod rem-exp-log rem-square-sqrt
2×expm1-log1p neg-sub0 expm1-udef unpow1/3 associate--r-
1×associate-+l+ remove-posit16 log1p-expm1 sub-div sqr-sin exp-to-pow hypot-udef rem-cbrt-cube rem-log-exp acos-asin sin-mult log1p-udef

regimes19.4s (1.7%)

Accuracy

Total 47.3b remaining (28.5%)

Threshold costs 5.4b (3.3%)

8.4b30.6%Toniolo and Linder, Equation (13)
7.1b42.3%Toniolo and Linder, Equation (10+)
6.7b1.2%Henrywood and Agarwal, Equation (12)
6.1b21.7%Henrywood and Agarwal, Equation (13)
5.1b78.1%Toniolo and Linder, Equation (7)

localize5.9s (0.5%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)