Details

sample4.4m (32.2%)

Algorithm
61×intervals
Results
1.1m252107×body80valid
56.7s29449×body1280valid
40.1s158999×body80nan
27.2s20074×body640valid
24.2s8862×body2560valid
14.0s3447×body5120valid
10.5s9912×body320valid
5.2s8973×body160valid
1.5s626×body10240exit
704.0ms627×body1280nan
466.0ms638×body640nan
315.0ms8256×pre80true
294.0ms361×body320nan
65.0ms194×body160nan

prune4.1m (30.3%)

simplify2.8m (20.3%)

series1.4m (10.0%)

Calls

427 calls:

2.4s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.9s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.7s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.6s
(fma (/ 3 (* t (* (sqrt 2) 2))) (/ (* v v) PI) (- (/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t) (fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI))))))
1.5s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*))))))

rewrite24.9s (3.0%)

Algorithm
114×rewrite-expression-head
Calls

427 calls:

2.4s
(* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ (/ 1 (cbrt l)) (cbrt l)))) (* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l)))))
1.7s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
1.5s
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (* (/ c0 h) (/ d D)) (/ (/ d D) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
891.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
798.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (posit16->real (real->posit16 (- l (fabs (- m n))))))
Rules
45235×times-frac
25517×add-sqr-sqrt
23578×*-un-lft-identity
22746×add-cube-cbrt
10551×sqrt-prod
7802×add-exp-log
6548×prod-diff
5972×add-cbrt-cube
5781×unpow-prod-up
3544×associate-*l*
3132×cbrt-prod
3081×div-exp
3007×prod-exp
2242×cbrt-unprod
2241×cbrt-undiv
2164×pow1
1876×div-inv
1306×associate-*r*
1091×associate-/l*
863×associate-/r*
674×associate-*r/
654×pow-prod-down
577×frac-times
550×sqrt-div
528×unswap-sqr
513×add-log-exp
500×unpow-prod-down
429×expm1-log1p-u
427×log1p-expm1-u insert-posit16
394×associate-*l/
355×pow-prod-up
312×difference-of-squares
226×sqr-pow
224×pow-exp
214×distribute-rgt-neg-in
210×distribute-rgt-in distribute-lft-in
208×1-exp
207×distribute-lft-neg-in distribute-lft-out-- associate-/r/
203×sub-neg
193×flip3-- flip--
172×pow-sqr
144×fma-neg
138×sqrt-pow1
136×*-commutative
133×pow-plus
129×swap-sqr
128×pow-unpow
126×tan-quot
109×frac-sub
108×distribute-lft-out
99×pow1/2
96×distribute-neg-in pow2
92×frac-2neg clear-num
88×pow-to-exp
86×pow1/3
80×rec-exp
75×rem-sqrt-square
68×distribute-neg-frac
51×associate-/l/
49×fma-udef
48×log-prod exp-sum
46×fma-def
44×exp-prod
43×flip-+ associate--l+ flip3-+
41×unpow2
35×associate--r+
34×diff-log
27×pow-pow
24×cbrt-div
23×neg-mul-1 cos-sum
17×pow-flip cube-unmult
12×frac-add pow-sub
11×sum-log +-commutative inv-pow
10×div-sub
hypot-def
neg-log un-div-inv
neg-sub0
remove-posit16 exp-diff distribute-rgt-neg-out associate--l-
associate-+r- exp-neg associate-+l- acos-asin associate--r- distribute-rgt-out--
associate-+l+ expm1-log1p expm1-udef associate-+r+ log1p-expm1 sqrt-unprod hypot-udef asin-acos rem-exp-log rem-square-sqrt log1p-udef
sqrt-undiv sub-div sqr-sin cos-diff sin-mult

regimes20.2s (2.5%)

Accuracy

Total 52.2b remaining (28.9%)

Threshold costs 4.3b (2.4%)

8.4b9.7%Toniolo and Linder, Equation (10+)
8.4b13.2%Toniolo and Linder, Equation (13)
8.2b2.2%Henrywood and Agarwal, Equation (12)
7.6b-1.1%Henrywood and Agarwal, Equation (13)
5.1b78.1%Toniolo and Linder, Equation (7)

bsearch8.2s (1.0%)

localize6.0s (0.7%)

end1.0ms (0.0%)