Details

simplify9.3m (39.0%)

prune8.5m (35.5%)

sample3.0m (12.6%)

Algorithm
61×intervals
Results
44.7s253614×body80valid
36.1s29575×body1280valid
27.4s160606×body80nan
18.9s20413×body640valid
16.4s8910×body2560valid
8.5s3411×body5120valid
7.2s10021×body320valid
2.8s8980×body160valid
1.1s768×body10240exit
821.0ms621×body1280nan
780.0ms650×body640nan
203.0ms8256×pre80true
110.0ms189×body160nan
102.0ms340×body320nan

series1.6m (6.8%)

Calls

430 calls:

10.5s
(sqrt (+ (* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2)))) (* U (* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l))))))))
2.0s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*)))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt 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 (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite1.0m (4.4%)

Algorithm
115×rewrite-expression-head
Calls

430 calls:

19.6s
(* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k)))
2.8s
(* (* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1)))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k)))
2.5s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.2s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
2.1s
(+ (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
150809×times-frac
74226×add-sqr-sqrt
72250×*-un-lft-identity
71459×add-cube-cbrt
29977×cbrt-prod
26284×unpow-prod-up
25934×prod-diff
10356×sqrt-prod
6804×add-exp-log
6360×div-inv
5382×associate-*l*
5088×add-cbrt-cube
3419×div-exp
2550×cbrt-undiv
2530×unpow-prod-down
2238×pow1
1844×prod-exp
1523×cbrt-unprod
1319×associate-*r*
1168×associate-/l*
1092×associate-/r*
1027×sqr-pow
887×associate-/r/
688×sub-neg
574×pow-prod-down
510×unswap-sqr
501×add-log-exp
471×pow-prod-up
431×log1p-expm1-u
430×expm1-log1p-u insert-posit16
263×tan-quot
242×cbrt-div distribute-lft-out--
231×difference-of-squares
222×pow-sqr
193×pow-plus
182×associate-*r/
156×distribute-rgt-neg-in
155×1-exp
153×distribute-lft-out
150×distribute-lft-neg-in
149×distribute-rgt-in distribute-lft-in
137×pow2
128×*-commutative
126×sqrt-div fma-neg
122×pow1/3
118×swap-sqr
114×flip3-- flip--
110×pow-unpow
109×frac-2neg clear-num
97×associate-*l/
86×sqrt-pow1
85×pow-exp
84×frac-times
70×rem-sqrt-square
69×pow1/2
62×pow-to-exp
59×associate-/l/
58×pow-sub
52×exp-prod
49×log-pow
41×log-prod
39×frac-sub fma-udef
35×associate--r+
34×associate--l+
32×fma-def frac-add
30×flip-+ flip3-+ diff-log
28×rec-exp unpow2
24×cos-sum
22×pow-pow
18×neg-mul-1
11×div-sub
10×pow-flip
exp-sum pow3 inv-pow
rem-log-exp
sum-log neg-log +-commutative
hypot-udef
neg-sub0 cube-unmult associate--l- un-div-inv exp-to-pow distribute-rgt-out-- asin-acos rem-exp-log acos-asin associate--r-
remove-posit16 sqrt-undiv unpow1/2 sqrt-unprod sub-div sqr-sin hypot-def rem-cbrt-cube sin-mult
expm1-log1p expm1-udef exp-diff log1p-expm1 sqrt-pow2 rem-square-sqrt cos-diff e-exp-1 log1p-udef

regimes18.1s (1.3%)

Accuracy

Total 54.6b remaining (32.9%)

Threshold costs 5.6b (3.4%)

10.3b23%Toniolo and Linder, Equation (13)
8.8b-2.2%Henrywood and Agarwal, Equation (13)
6.3b-4.8%Given's Rotation SVD example
5.3b77.2%Toniolo and Linder, Equation (7)
4.2b0%Maksimov and Kolovsky, Equation (3)

localize5.6s (0.4%)

bsearch1.5s (0.1%)

end1.0ms (0.0%)