Details

simplify19.4m (55.2%)

prune7.1m (20.1%)

sample4.2m (11.9%)

Algorithm
60×intervals
Results
59.7s248059×body80valid
51.3s27527×body1280valid
41.9s160919×body80nan
24.4s18640×body640valid
22.0s8652×body2560valid
14.6s3469×body5120valid
7.9s8890×body320valid
5.4s8566×body160valid
1.9s833×body10240exit
1.2s344×body320nan
851.0ms8256×pre80true
725.0ms623×body1280nan
641.0ms653×body640nan
67.0ms184×body160nan

rewrite2.7m (7.5%)

Algorithm
116×rewrite-expression-head
Calls

432 calls:

35.0s
(* (/ (/ (sqrt (sqrt 2)) (/ (cbrt t) 1)) (/ (tan k) (/ (sqrt (sqrt 2)) (/ (cbrt t) (/ l t))))) (/ (/ (sqrt 2) (* (/ (cbrt t) (/ l t)) (sin k))) (fma (/ k t) (/ k t) 2)))
2.1s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))
2.0s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (cbrt h)) (* (/ (* M D) (* d 2)) (cbrt h)))) (/ (cbrt h) l))
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)))
1.6s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
Rules
2949673×times-frac
1123660×add-sqr-sqrt
1119069×*-un-lft-identity
1117989×add-cube-cbrt
916893×sqrt-prod
460590×associate-*l*
401727×cbrt-prod
62999×div-inv
9490×add-exp-log
9264×associate-/r/
6603×add-cbrt-cube
4110×prod-exp
3838×prod-diff
3661×div-exp
3034×unpow-prod-up
2955×cbrt-unprod
2516×cbrt-undiv
2064×associate-/r*
1888×pow1
1378×associate-*r*
1149×difference-of-squares
842×unswap-sqr
776×associate-*l/
710×associate-/l*
546×pow-prod-down
511×frac-times
470×add-log-exp
460×pow-exp
457×associate-*r/
434×expm1-log1p-u
432×log1p-expm1-u insert-posit16
338×pow-to-exp
312×sqrt-div
303×1-exp
295×unpow-prod-down
235×pow-prod-up
208×flip3-- flip--
153×rec-exp
149×sqr-pow
147×pow-sqr
132×*-commutative
118×pow-unpow
116×pow-plus
109×frac-2neg clear-num
108×sqrt-pow1
102×sub-neg
89×swap-sqr
86×pow2
85×distribute-lft-out
69×distribute-lft-out--
68×pow1/3
66×pow1/2
61×rem-sqrt-square
60×distribute-rgt-in distribute-lft-in
59×cbrt-div
55×flip-+ flip3-+
51×fma-def fma-neg
46×neg-mul-1 distribute-rgt-neg-in distribute-lft-neg-in
41×associate-/l/
40×exp-prod
34×tan-quot
32×frac-add
29×fma-udef
26×log-prod
25×distribute-rgt-out-- pow-pow
23×unpow2
21×pow-flip
20×log-pow
19×inv-pow
18×pow-sub
15×cos-sum
sum-log +-commutative diff-log
exp-sum un-div-inv
div-sub
rem-log-exp
acos-asin
remove-posit16 cube-prod frac-sub asin-acos rem-exp-log cos-diff
expm1-log1p expm1-udef associate-+r- associate-+r+ associate--l+ log1p-expm1 distribute-neg-frac hypot-udef hypot-def log1p-udef
rem-cube-cbrt exp-diff sqrt-undiv unpow3 sqrt-unprod sub-div sqr-sin exp-to-pow rem-square-sqrt cube-mult sin-mult

series1.4m (4.0%)

Calls

432 calls:

2.5s
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.4s
(sqrt (* (* (* (* U 2) n) (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
2.2s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.1s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes19.8s (0.9%)

Accuracy

Total 47.8b remaining (29.3%)

Threshold costs 2.7b (1.7%)

10.6b11.9%Toniolo and Linder, Equation (13)
7.1b34.1%Toniolo and Linder, Equation (10-)
6.5b22.3%Henrywood and Agarwal, Equation (13)
5.3b77.2%Toniolo and Linder, Equation (7)
4.0b0%Maksimov and Kolovsky, Equation (3)

localize6.2s (0.3%)

bsearch2.3s (0.1%)

end1.0ms (0.0%)