Details

simplify19.6m (54.9%)

prune9.9m (27.8%)

sample3.6m (10.2%)

Algorithm
58×intervals
Results
1.0m248745×body80valid
41.0s159692×body80nan
33.7s21557×body1280valid
19.6s8502×body10240exit
17.7s14718×body640valid
8.4s5807×body2560valid
8.0s7655×body320valid
5.3s2434×body5120valid
3.8s8297×body160valid
628.0ms597×body1280nan
527.0ms664×body640nan
349.0ms8256×pre80true
212.0ms320×body320nan
79.0ms219×body160nan

series1.5m (4.1%)

Calls

441 calls:

Slowest
1.9s
(* (* (/ (/ (cbrt 2) (cbrt (tan k))) (/ (* (fma (/ k t) (/ k t) 2) t) (/ (cbrt 2) (cbrt (tan k))))) (/ l t)) (/ (* (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k)))) (/ (cbrt (cbrt 2)) (cbrt (cbrt (tan k))))) (* (cbrt (sin k)) (cbrt (sin k)))))
1.8s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.5s
(* (* (* (pow (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h))) 1/2) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (* h (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* 2 l))))

rewrite37.1s (1.7%)

Algorithm
117×rewrite-expression-head
Calls

441 calls:

Slowest
3.1s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)))
3.1s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)))
1.5s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.4s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.4s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
Rules
87984×times-frac
45715×add-exp-log
40472×*-un-lft-identity
38870×add-sqr-sqrt
37884×add-cube-cbrt
24295×div-exp
23513×cbrt-prod
20236×add-cbrt-cube
18352×prod-exp
16260×cbrt-undiv
11474×cbrt-unprod
11412×associate-*r*
10961×sqrt-prod
3413×associate-*l*
3151×div-inv
2667×1-exp
1439×pow1
1347×associate-/r/
1224×prod-diff
1173×rec-exp
1137×associate-/l*
1107×distribute-lft-out
830×associate-/r*
534×sqrt-div
492×distribute-neg-in
485×add-log-exp
449×associate-*r/
442×log1p-expm1-u
441×expm1-log1p-u insert-posit16
434×distribute-rgt-in distribute-lft-in
419×fma-def
401×pow-prod-down
357×cbrt-div
344×pow-exp
306×tan-quot
294×exp-sum
268×log-prod
257×pow-unpow
249×unswap-sqr
201×distribute-lft-out--
186×sqrt-pow1
180×frac-times
179×unpow-prod-down
176×associate-*l/
175×flip3-- flip--
171×difference-of-squares
152×flip-+ flip3-+
133×pow1/2
130×pow-prod-up
128×frac-2neg clear-num
125×*-commutative
114×pow-to-exp
94×swap-sqr
84×sqr-pow
70×fma-neg
67×rem-sqrt-square
66×associate-/l/
62×pow-sqr
59×sub-neg
58×fma-udef
54×log-pow
47×pow-plus
35×exp-prod
34×pow2
27×pow1/3
25×div-sub frac-add
22×pow-pow
20×un-div-inv
15×pow-flip
13×pow-sub
12×associate--l+
11×frac-sub diff-log
10×sum-log +-commutative inv-pow unpow2 cos-sum
hypot-def
sqrt-unprod rem-log-exp
rem-square-sqrt acos-asin
associate-+r- hypot-udef asin-acos
expm1-log1p expm1-udef cube-unmult exp-to-pow cos-diff
neg-sub0 remove-posit16 exp-diff sqrt-undiv exp-neg sin-mult sub-div sqr-sin rem-exp-log

regimes17.4s (0.8%)

Accuracy

Total 44.2b remaining (29.2%)

Threshold costs 3.6b (2.4%)

8.7b24.1%Toniolo and Linder, Equation (13)
8.0b12.2%Henrywood and Agarwal, Equation (13)
7.6b41.9%Henrywood and Agarwal, Equation (3)
5.1b78.1%Toniolo and Linder, Equation (7)
4.9b17.1%Henrywood and Agarwal, Equation (12)

localize7.0s (0.3%)

bsearch1.6s (0.1%)

end1.0ms (0.0%)