Details

simplify8.4m (41.2%)

prune6.7m (32.5%)

sample3.0m (14.7%)

Algorithm
61×intervals
Results
44.0s252279×body80valid
36.0s29162×body1280valid
29.7s160850×body80nan
18.0s20247×body640valid
15.0s8741×body2560valid
9.5s3344×body5120valid
7.1s10056×body320valid
3.6s9093×body160valid
1.4s864×body10240exit
403.0ms662×body1280nan
285.0ms645×body640nan
195.0ms8256×pre80true
146.0ms365×body320nan
36.0ms194×body160nan

series1.4m (7.0%)

Calls

435 calls:

2.5s
(fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (/ M (/ (* 2 d) D)) (/ h l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h))))
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))))
1.8s
(/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
1.8s
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.6s
(/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))

rewrite26.9s (2.2%)

Algorithm
115×rewrite-expression-head
Calls

435 calls:

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)))
1.5s
(+ (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)))
1.4s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.3s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
Rules
113160×times-frac
52515×add-sqr-sqrt
49990×*-un-lft-identity
49302×add-cube-cbrt
26709×cbrt-prod
7864×sqrt-prod
7729×add-exp-log
6403×prod-diff
5699×unpow-prod-up
5452×add-cbrt-cube
5199×associate-*l*
4756×div-inv
4011×div-exp
2822×cbrt-undiv
2099×prod-exp
1918×pow1
1773×associate-*r*
1695×cbrt-unprod
1425×associate-/r*
1079×associate-/l*
884×unpow-prod-down
846×associate-/r/
604×unswap-sqr
546×add-log-exp
522×pow-prod-down
438×log1p-expm1-u
436×expm1-log1p-u
435×insert-posit16
357×sqr-pow
286×swap-sqr
265×pow-prod-up
257×1-exp
249×difference-of-squares
231×associate-*r/
218×cbrt-div
216×distribute-lft-out--
212×tan-quot
197×distribute-rgt-neg-in
191×distribute-lft-neg-in
187×sub-neg
168×sqrt-div
164×distribute-rgt-in distribute-lft-in
157×pow-sqr
152×associate-*l/
144×sqrt-pow1
139×frac-times
138×pow-exp
133×exp-sum
130×pow-plus
126×flip3-- flip--
121×*-commutative
108×pow1/2
107×frac-2neg clear-num
106×fma-neg
88×pow2
83×distribute-lft-out
77×rec-exp
72×pow1/3 flip-+ flip3-+
71×pow-to-exp
69×cos-sum rem-sqrt-square
67×fma-def
64×associate-/l/
58×exp-prod fma-udef
54×pow-unpow
51×associate-+l+
43×pow-sub
41×unpow2
40×frac-add
32×associate--r+
30×sum-log diff-log
26×pow-pow
21×neg-mul-1
20×sqrt-undiv
19×+-commutative distribute-neg-frac
14×hypot-def
12×associate--l+
10×frac-sub sqrt-unprod
pow-flip div-sub
inv-pow rem-exp-log
pow3 neg-log
associate-+r+ rem-square-sqrt acos-asin
expm1-log1p expm1-udef distribute-lft-neg-out cube-unmult remove-posit16
neg-sub0 exp-diff distribute-rgt-out-- hypot-udef asin-acos cos-diff associate--r-
associate--l- distribute-rgt-neg-out log1p-expm1 sqrt-pow2 sqr-sin un-div-inv rem-cbrt-cube sin-mult log1p-udef
sub-div pow-neg

regimes18.3s (1.5%)

Accuracy

Total 56.4b remaining (31.5%)

Threshold costs 4.5b (2.5%)

13.9b-4.8%Toniolo and Linder, Equation (13)
8.8b-0.4%Henrywood and Agarwal, Equation (13)
6.6b49.9%Henrywood and Agarwal, Equation (3)
6.2b74.3%Toniolo and Linder, Equation (7)
4.4b-9.1%Maksimov and Kolovsky, Equation (3)

localize5.7s (0.5%)

bsearch5.2s (0.4%)

end1.0ms (0.0%)