Details

prune2.7m (39.6%)

series1.8m (26.3%)

Calls

429 calls:

5.1s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

sample1.3m (19.8%)

Algorithm
61×intervals
Results
16.0s253099×body80valid
15.4s29318×body1280valid
9.9s159299×body80nan
8.6s8984×body2560valid
7.0s20018×body640valid
5.1s3415×body5120valid
2.4s10071×body320valid
1.3s8932×body160valid
436.0ms638×body10240exit
152.0ms620×body1280nan
123.0ms640×body640nan
111.0ms8256×pre80true
50.0ms341×body320nan
20.0ms188×body160nan

rewrite22.9s (5.7%)

Algorithm
115×rewrite-expression-head
Calls

429 calls:

1.4s
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
1.0s
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2))) (/ (/ (cos k) (/ 1 l)) (pow (cbrt (sin k)) 2)))
804.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
511.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (/ 1 (/ (pow (cbrt (sin k)) 4) l)) (pow (cbrt 1) 2)))
474.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI (* t (* (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))))) (cbrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
Rules
153774×add-exp-log
112101×div-exp
67551×prod-exp
55329×pow-exp
35802×times-frac
33536×pow-to-exp
17851×rec-exp 1-exp
17532×add-sqr-sqrt
16109×*-un-lft-identity
15531×add-cube-cbrt
10546×unpow-prod-down
5984×associate-*r*
5661×cbrt-prod
2289×add-cbrt-cube
2031×sqr-pow
1256×pow1
1161×associate-*r/
933×cbrt-unprod
871×unpow2
818×associate-*l*
786×sqrt-prod
649×div-inv
613×associate-/l*
611×sqrt-div
593×unswap-sqr
468×frac-times
467×cbrt-div
465×add-log-exp
444×cbrt-undiv
435×pow-prod-down
431×log1p-expm1-u expm1-log1p-u
397×flip-- flip3--
344×associate-*l/
308×prod-diff
305×associate-/r*
297×pow-unpow
260×associate-/r/
222×distribute-rgt-in distribute-lft-in
210×distribute-lft-out--
143×*-commutative
130×exp-prod
111×distribute-lft-neg-in distribute-rgt-neg-in
108×difference-of-squares
104×sqrt-pow1
89×cube-prod
80×frac-2neg clear-num
77×flip-+ flip3-+
72×pow1/3 tan-quot
71×pow1/2
69×hypot-def
62×associate--l+
60×distribute-lft-out
57×sub-neg
46×rem-sqrt-square pow-pow
43×associate-/l/
42×swap-sqr
36×fma-def
33×fma-udef frac-sub
27×cos-sum
25×pow-prod-up
24×fma-neg
22×div-sub
21×pow-sqr
15×neg-mul-1
14×pow-sub
12×log-prod
11×unpow3 cube-mult
10×exp-neg log-pow
9×+-commutative sum-log
8×diff-log un-div-inv distribute-rgt-neg-out
7×pow-plus neg-sub0
6×exp-sum
5×pow2 acos-asin rem-cbrt-cube
4×cube-div rem-exp-log mul-1-neg pow-neg log1p-udef log1p-expm1 frac-add expm1-log1p expm1-udef distribute-frac-neg distribute-neg-frac log-rec
3×unpow-prod-up hypot-udef
2×exp-diff sqrt-unprod rem-square-sqrt associate-+r+
1×rem-cube-cbrt e-exp-1 asin-acos inv-pow sum-cubes cos-diff pow-flip mul0 rem-log-exp

simplify18.6s (4.6%)

Algorithm
175×egg-herbie

regimes11.1s (2.7%)

Accuracy

Total 41.9b remaining (23%)

Threshold costs 4.6b (2.5%)

11.2b14.9%Toniolo and Linder, Equation (13)
9.2b1.7%Henrywood and Agarwal, Equation (12)
5.4b77.4%Toniolo and Linder, Equation (7)
4.2b18.2%Toniolo and Linder, Equation (10-)
4.1b45.2%Toniolo and Linder, Equation (10+)

bsearch2.9s (0.7%)

localize2.2s (0.6%)

end1.0ms (0.0%)