Details

simplify9.3m (50.0%)

sample4.4m (23.7%)

Algorithm
61×intervals
Results
1.0m252624×body80valid
54.8s28799×body1280valid
42.2s160368×body80nan
30.3s20582×body640valid
23.2s8763×body2560valid
14.7s3433×body5120valid
11.9s10107×body320valid
5.1s9126×body160valid
1.7s640×body10240exit
785.0ms638×body1280nan
675.0ms8256×pre80true
560.0ms631×body640nan
224.0ms356×body320nan
72.0ms199×body160nan

prune2.6m (13.8%)

series1.5m (7.8%)

Calls

432 calls:

2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.6s
(sqrt (* (* U 2) (* (* (cbrt n) (cbrt n)) (* (cbrt n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
2.6s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (cbrt l) (cbrt l)) (/ n (/ Om (cbrt l)))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.5s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite23.3s (2.1%)

Algorithm
115×rewrite-expression-head
Calls

432 calls:

2.2s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))
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)))
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)))
1.3s
(+ (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
18706×times-frac
12588×add-sqr-sqrt
12394×*-un-lft-identity
11171×add-cube-cbrt
8047×add-exp-log
6482×add-cbrt-cube
5016×sqrt-prod
3784×prod-exp
3509×prod-diff
3413×cbrt-unprod
3371×cbrt-prod
3280×unpow-prod-up
2449×div-exp
2206×cbrt-undiv
1993×associate-*l*
1639×pow1
1073×associate-*r*
965×associate-/r*
822×associate-/l*
752×div-inv
704×associate-*l/
561×frac-times
521×associate-*r/
518×pow-prod-down
512×add-log-exp
509×distribute-lft-out
455×associate-/r/
433×expm1-log1p-u log1p-expm1-u
432×insert-posit16
410×unswap-sqr
390×unpow-prod-down
322×exp-prod
271×swap-sqr
224×distribute-lft-out--
185×pow1/3
179×pow-prod-up
163×difference-of-squares
162×sqr-pow
160×pow-exp
141×*-commutative
127×sqrt-div flip-+ flip3-+
118×sub-neg
115×pow-unpow cbrt-div
108×frac-add
105×flip3-- flip--
97×pow-sqr
95×sqrt-pow1 pow-plus
94×frac-2neg clear-num
83×distribute-rgt-in distribute-lft-in
77×fma-def
69×pow-to-exp
63×pow2
56×fma-neg
53×pow1/2
47×rem-sqrt-square
46×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
44×1-exp rec-exp
39×associate-/l/
35×cos-sum
33×fma-udef
30×unpow2
28×sum-log
27×tan-quot
23×pow-pow
15×+-commutative pow-sub
13×associate-+r+
12×diff-log
10×div-sub
8×pow-flip associate-+r- pow3 inv-pow
7×rem-exp-log cos-diff
5×associate-+l+ exp-diff
4×frac-sub distribute-rgt-out-- difference-of-sqr-1 asin-acos
3×expm1-log1p expm1-udef log-prod un-div-inv log-pow
2×associate--l+ distribute-neg-frac hypot-def unpow1/3
1×log1p-expm1 sqrt-unprod sub-div sqr-sin exp-to-pow hypot-udef rem-square-sqrt rem-cbrt-cube rem-log-exp acos-asin sin-mult log1p-udef

regimes19.3s (1.7%)

Accuracy

Total 39.1b remaining (25.7%)

Threshold costs 5.7b (3.8%)

6.7b33.9%Toniolo and Linder, Equation (10-)
6.4b20.9%Henrywood and Agarwal, Equation (13)
5.5b40.3%Toniolo and Linder, Equation (13)
5.1b78%Toniolo and Linder, Equation (7)
3.9b0%Maksimov and Kolovsky, Equation (3)

localize6.4s (0.6%)

bsearch2.8s (0.3%)

end1.0ms (0.0%)