Details

prune5.7m

sample4.6m

Algorithm
60×intervals
Results
1.1m258000×body80valid
54.0s28075×body1280valid
43.4s161035×body80nan
26.1s19032×body640valid
20.2s8677×body10240exit
18.2s7995×body2560valid
14.4s3440×body5120valid
9.1s9567×body320valid
5.0s9049×body160valid
975.0ms627×body640nan
608.0ms607×body1280nan
602.0ms350×body320nan
371.0ms8256×pre80true
179.0ms197×body160nan

simplify3.9m

series1.5m

Calls

450 calls:

Slowest
2.7s
(sqrt (* (* (* (* U 2) n) (* (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
2.3s
(sqrt (* (* (* (* U 2) n) (* (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
2.1s
(sqrt (* (* (* U 2) n) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.1s
(sqrt (* (* (* (* U 2) n) (* (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))) (cbrt (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
1.9s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite24.3s

Algorithm
116×rewrite-expression-head
Calls

450 calls:

Slowest
2.9s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)))
1.3s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.3s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.2s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
1.1s
(+ (sqrt (- (* (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h)) (* M M))) (/ (/ (* (* c0 (/ d D)) (/ d D)) w) h))
Rules
14592×times-frac
10008×add-sqr-sqrt
9562×*-un-lft-identity
8666×add-cube-cbrt
7069×add-exp-log
4234×add-cbrt-cube
3001×prod-exp
2945×sqrt-prod
2404×div-exp
1848×prod-diff
1662×pow1
1446×cbrt-undiv
1427×cbrt-unprod
1364×associate-*r*
1087×associate-*l*
888×div-inv
753×associate-/l*
729×associate-/r*
568×difference-of-squares
564×pow-exp
542×add-log-exp
531×cbrt-prod
511×pow-prod-down
450×expm1-log1p-u log1p-expm1-u insert-posit16
336×associate-*r/
328×unpow-prod-up
322×unpow-prod-down
304×unswap-sqr
281×distribute-lft-out--
249×pow-to-exp
226×associate-*l/
223×distribute-rgt-in distribute-lft-in
221×1-exp
206×associate-/r/
197×flip3-- flip--
179×pow-unpow
178×cbrt-div
175×sqrt-div
174×exp-prod
161×frac-times
153×fma-neg
148×*-commutative
147×pow-prod-up
143×rec-exp
125×frac-2neg clear-num
123×sqr-pow
110×exp-sum fma-def
100×distribute-lft-out
92×swap-sqr
90×sqrt-pow1
86×log-prod
72×sub-neg
71×pow-sqr
70×pow-plus
66×flip-+ flip3-+
55×associate-/l/
54×pow1/2
52×pow2
46×rem-sqrt-square
44×tan-quot
33×pow1/3
32×pow-pow frac-add
31×pow-flip
29×fma-udef
24×log-pow
22×sum-log
21×diff-log
19×inv-pow
18×+-commutative
14×div-sub
pow-sub
rem-exp-log
exp-diff frac-sub hypot-udef
associate-+r+ unpow2
cube-unmult sub-div un-div-inv cos-sum
associate-+r- difference-of-sqr-1 acos-asin
remove-posit16 rem-log-exp distribute-rgt-out-- asin-acos cos-diff
associate-+l+ associate--l+ pow-div pow3 sqrt-unprod associate--r+ exp-to-pow hypot-def
expm1-log1p expm1-udef sqrt-undiv unpow1/2 sqr-sin sin-mult log-div

regimes18.0s

Accuracy

Total 44.0b remaining (29.2%)

Threshold costs 4.2b (2.8%)

9.8b18.1%Toniolo and Linder, Equation (13)
9.0b0%Henrywood and Agarwal, Equation (13)
6.5b5.5%Henrywood and Agarwal, Equation (12)
5.4b77.3%Toniolo and Linder, Equation (7)
4.0b-3.6%Maksimov and Kolovsky, Equation (3)

localize5.9s

bsearch4.6s

end1.0ms