Details

simplify8.1m (46.6%)

prune3.7m (21.2%)

sample3.3m (18.7%)

Algorithm
61×intervals
Results
46.6s252736×body80valid
40.3s29428×body1280valid
27.8s159195×body80nan
20.8s20197×body640valid
18.7s8725×body2560valid
11.7s3555×body5120valid
6.6s9981×body320valid
3.3s9165×body160valid
1.1s623×body10240exit
688.0ms637×body640nan
513.0ms644×body1280nan
205.0ms8256×pre80true
102.0ms321×body320nan
77.0ms197×body160nan

series1.5m (8.4%)

Calls

446 calls:

3.0s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))) (* 2 n)))
3.0s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))) (* 2 n)))
2.6s
(sqrt (* (* U (fma (* (/ (/ (* l l) Om) Om) (- U* U)) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))
2.5s
(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite22.0s (2.1%)

Algorithm
119×rewrite-expression-head
Calls

446 calls:

1.8s
(* (/ (/ (* (/ (/ (cbrt 2) (cbrt t)) (cbrt (tan k))) (/ (/ (cbrt 2) (cbrt t)) (cbrt (tan k)))) (/ k (/ l 1))) (/ k (/ l 1))) (/ (/ (/ (cbrt 2) (cbrt t)) (cbrt (tan k))) (sin k)))
1.8s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.7s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
39626×times-frac
22335×add-sqr-sqrt
19846×*-un-lft-identity
19398×add-cube-cbrt
13663×sqrt-prod
11066×add-exp-log
6923×div-exp
6481×add-cbrt-cube
6125×prod-diff
5731×unpow-prod-up
4394×cbrt-undiv
3685×associate-*l*
2458×prod-exp
2178×cbrt-prod
1790×cbrt-unprod
1647×associate-*r*
1621×div-inv
1217×associate-/l*
1184×pow1
663×associate-/r*
550×unswap-sqr
510×add-log-exp
480×swap-sqr
448×expm1-log1p-u log1p-expm1-u
446×insert-posit16
359×1-exp
333×pow-prod-down
265×unpow-prod-down
261×associate-/r/
225×sqr-pow
199×sub-neg
184×cos-sum
170×sqrt-div
133×flip3-- flip--
131×frac-times distribute-rgt-in distribute-lft-in
121×associate-*r/
119×*-commutative
117×associate-*l/
116×difference-of-squares
113×sqrt-pow1
111×frac-2neg clear-num
107×distribute-lft-out--
90×pow1/3
86×pow-unpow
78×pow1/2
73×distribute-lft-out pow-exp
67×rem-sqrt-square
64×fma-neg
61×associate-/l/
55×fma-udef
45×fma-def
44×pow-prod-up
43×log-prod
35×pow-to-exp log-pow tan-quot
32×pow-sqr
27×unpow2
25×rec-exp
24×pow-pow frac-add
23×flip-+ flip3-+
22×exp-prod
21×cbrt-div pow-plus diff-log
17×pow2
16×exp-sum
13×sum-log div-sub
12×pow-sub
8×+-commutative cos-diff
7×pow-flip inv-pow rem-log-exp
5×acos-asin
4×associate--l+ log1p-expm1 log1p-udef hypot-def
3×expm1-udef remove-posit16 associate--r+ asin-acos hypot-udef
2×expm1-log1p frac-sub pow3 difference-of-sqr-1 sqrt-unprod rem-square-sqrt expm1-def
1×cube-unmult sub-div un-div-inv exp-to-pow rem-cbrt-cube

regimes21.3s (2.0%)

Accuracy

Total 48.8b remaining (28.4%)

Threshold costs 4.1b (2.4%)

8.4b20.9%Toniolo and Linder, Equation (13)
7.2b51.3%Henrywood and Agarwal, Equation (3)
7.2b13.5%Henrywood and Agarwal, Equation (13)
6.2b74.4%Toniolo and Linder, Equation (7)
4.4b32%Toniolo and Linder, Equation (10+)

localize6.6s (0.6%)

bsearch2.6s (0.2%)

end1.0ms (0.0%)