Details

simplify8.4m (38.9%)

prune6.6m (30.6%)

sample4.2m (19.3%)

Algorithm
61×intervals
Results
1.0m252525×body80valid
52.3s28971×body1280valid
40.7s160588×body80nan
27.6s19841×body640valid
19.2s8851×body2560valid
11.9s3470×body5120valid
8.7s10000×body320valid
4.6s9047×body160valid
1.7s869×body10240exit
679.0ms592×body1280nan
500.0ms582×body640nan
422.0ms380×body320nan
266.0ms8256×pre80true
69.0ms202×body160nan

series1.5m (6.7%)

Calls

443 calls:

2.4s
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
2.0s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))

rewrite28.9s (2.2%)

Algorithm
117×rewrite-expression-head
Calls

443 calls:

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)))
1.7s
(cbrt (* (/ (* (sqrt (fma (* v v) -3 1)) (sqrt 2)) 4) (* (/ (* (sqrt (fma (* v v) -3 1)) (sqrt 2)) 4) (* (* (* (- 1 (* v v)) (- 1 (* v v))) (- 1 (* v v))) (/ (* (sqrt (fma (* v v) -3 1)) (sqrt 2)) 4)))))
1.6s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.4s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.2s
(* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k)))
Rules
111525×times-frac
50786×add-sqr-sqrt
48542×*-un-lft-identity
47876×add-cube-cbrt
30265×cbrt-prod
8975×add-exp-log
6126×add-cbrt-cube
6007×sqrt-prod
6005×associate-*l*
4423×div-inv
4279×div-exp
2951×prod-exp
2866×cbrt-undiv
2642×prod-diff
2111×cbrt-unprod
1695×unpow-prod-up
1548×associate-*r*
1438×associate-/l*
1433×pow1
1202×associate-/r*
1030×frac-times
877×associate-*r/
837×associate-/r/
576×unswap-sqr
557×flip3-- flip--
556×associate-*l/
518×add-log-exp
459×cbrt-div
446×expm1-log1p-u log1p-expm1-u
443×insert-posit16
406×pow-prod-down unpow-prod-down
358×1-exp
261×tan-quot
226×sqrt-div
208×difference-of-squares
203×distribute-lft-out--
177×swap-sqr
172×distribute-rgt-in distribute-lft-in
156×distribute-rgt-neg-in
152×fma-neg
150×frac-sub distribute-lft-neg-in sqr-pow
140×sqrt-pow1
135×*-commutative
116×pow-prod-up
108×frac-2neg clear-num sub-neg
105×pow1/3
104×distribute-lft-out
98×pow-exp
88×pow1/2
86×rec-exp
80×pow-sqr
63×rem-sqrt-square
62×pow-to-exp
56×pow-plus
52×associate--l+
50×associate-/l/
46×pow2
43×unpow2
41×pow-unpow
38×fma-def
33×associate--r+ fma-udef
32×diff-log
24×cos-sum
19×pow-sub
18×pow-flip flip-+ pow-pow neg-mul-1 flip3-+ frac-add
10×inv-pow
9×sum-log
8×hypot-udef
7×+-commutative un-div-inv
6×expm1-log1p expm1-udef neg-log
5×remove-posit16 div-sub
4×acos-asin
3×neg-sub0 associate--l- log1p-expm1 sqrt-unprod asin-acos associate--r- log1p-udef
2×associate-+r+ pow-div distribute-rgt-out-- rem-square-sqrt
1×associate-+l+ pow3 sub-div sqr-sin remove-double-div cos-diff sin-mult

regimes21.3s (1.6%)

Accuracy

Total 45.5b remaining (26.6%)

Threshold costs 4.1b (2.4%)

10.4b3.2%Toniolo and Linder, Equation (13)
9.3b-7.9%Henrywood and Agarwal, Equation (13)
5.2b77.6%Toniolo and Linder, Equation (7)
4.1b0.2%Maksimov and Kolovsky, Equation (3)
3.3b0%Henrywood and Agarwal, Equation (12)

localize5.8s (0.5%)

bsearch2.8s (0.2%)

end0.0ms (0.0%)