Details

prune26.7m (45.1%)

rewrite14.0m (23.6%)

Algorithm
116×rewrite-expression-head
Calls

438 calls:

6.5m
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.7m
(* (* (* (/ (/ (* M D) 2) d) (/ (/ 1 (sqrt 2)) 1)) (* (/ (/ (* M D) (sqrt 2)) d) h)) (/ 1 l))
11.0s
(* (* (* (/ (/ (* M D) 2) d) (/ (/ (* M D) 2) d)) h) (/ 1 l))
10.6s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
10.5s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
Rules
300265×add-sqr-sqrt
231855×times-frac
219147×frac-times
180129×*-un-lft-identity
177774×associate-/l*
168012×add-cube-cbrt
115705×associate-/r*
76631×associate-*r*
70800×associate-*l*
61666×associate-*l/
53382×unswap-sqr
47853×associate-/l/
36231×cbrt-prod
20718×swap-sqr
20077×clear-num
19733×frac-2neg
17228×*-commutative
17123×associate-*r/
14723×difference-of-squares
11789×sqrt-prod
10240×sqrt-div
9394×cbrt-div
9108×prod-diff
8188×div-inv
7124×distribute-lft-out--
6269×add-exp-log
5114×add-cbrt-cube
4766×flip3-- flip--
3220×frac-sub
3124×frac-add
2753×associate-/r/
2458×div-exp
2425×fma-def
2331×prod-exp
2215×distribute-rgt-in distribute-lft-in
1960×unpow-prod-down
1954×cbrt-unprod
1904×cbrt-undiv
1712×unpow-prod-up
1419×distribute-rgt-out--
1396×pow1
1324×distribute-lft-out
984×associate--l+
785×un-div-inv
606×tan-quot
507×add-log-exp
440×log1p-expm1-u
436×expm1-log1p-u
434×insert-posit16
410×pow-prod-down
403×sqr-pow
243×1-exp
239×fma-neg
156×distribute-rgt-neg-in
150×distribute-lft-neg-in
132×cos-sum
126×unpow2
122×exp-diff log-div
111×sqrt-pow1 associate--r+
109×rec-exp
103×pow-prod-up rem-sqrt-square
99×pow1/3
98×sub-neg
94×pow-exp
85×pow-sub
78×log-prod exp-sum pow1/2
71×pow-sqr
70×pow-unpow
64×associate-+r+ difference-of-sqr-1
62×div-sub
61×pow-to-exp
53×pow-plus
46×associate-+l+
45×fma-udef
43×pow2
33×diff-log
21×pow-pow
18×+-commutative neg-mul-1
16×flip-+ flip3-+
12×pow-flip
9×expm1-log1p hypot-udef
7×sum-log sub-div
6×expm1-udef neg-log inv-pow exp-prod
5×remove-posit16 remove-double-div
4×pow3 associate--l- acos-asin
3×neg-sub0 asin-acos log-pow associate--r-
2×log1p-expm1 pow-div rem-exp-log rem-cbrt-cube log1p-udef
1×sqrt-unprod sqr-sin rem-square-sqrt cos-diff sin-mult

simplify12.2m (20.6%)

sample3.9m (6.5%)

Algorithm
59×intervals
Results
55.7s236482×body80valid
52.1s28055×body1280valid
34.3s144332×body80nan
28.5s19403×body640valid
19.7s7135×body2560valid
9.0s1144×body5120valid
8.3s9779×body320valid
4.7s8931×body160valid
581.0ms266×body10240exit
578.0ms8256×pre80true
576.0ms592×body1280nan
495.0ms582×body640nan
208.0ms380×body320nan
62.0ms202×body160nan

series2.0m (3.4%)

Calls

434 calls:

20.5s
(sqrt (* (* (cbrt n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
11.9s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
11.8s
(sqrt (* (cbrt (* (cbrt n) U)) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
2.0s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(fma (/ 3 t) (/ (* v v) (* PI (* 2 (sqrt 2)))) (- (/ (* 27/2 (/ (* (* v v) (* v v)) t)) (* (pow (sqrt 2) 5) PI)) (fma 4 (* (/ (* v v) (* PI (sqrt 2))) (/ (* v v) t)) (fma (/ 4 (* PI (sqrt 2))) (/ (* v v) t) (* 12 (* (/ (* v v) (* PI (* 2 (sqrt 2)))) (/ (* v v) t)))))))

regimes16.2s (0.5%)

Accuracy

Total 31.8b remaining (23.8%)

Threshold costs 3.5b (2.6%)

5.6b0%Toniolo and Linder, Equation (13)
5.3b77.4%Toniolo and Linder, Equation (7)
4.3b-5.1%Toniolo and Linder, Equation (10+)
4.0b0.1%Maksimov and Kolovsky, Equation (3)
2.7b6.2%Toniolo and Linder, Equation (10-)

localize6.3s (0.2%)

bsearch2.2s (0.1%)

end1.0ms (0.0%)