Details

simplify7.9m (39.7%)

prune6.2m (30.8%)

sample3.1m (15.4%)

Algorithm
61×intervals
Results
45.4s252688×body80valid
36.1s29140×body1280valid
29.4s159687×body80nan
19.7s19941×body640valid
15.8s8642×body2560valid
8.9s3369×body5120valid
6.6s9714×body320valid
3.6s9202×body160valid
1.1s689×body10240exit
771.0ms593×body640nan
320.0ms571×body1280nan
285.0ms8256×pre80true
207.0ms369×body320nan
82.0ms200×body160nan

series1.6m (7.8%)

Calls

438 calls:

3.5s
(fma (sqrt (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M))) (- (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h))) (* M M)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)) (* (/ (* c0 (/ d D)) w) (/ (/ d D) h)))))
3.5s
(/ (/ (sqrt (/ (fma (* v v) -5 1) (sqrt PI))) t) (sqrt (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))))
2.8s
(/ (/ (sqrt (/ (fma (* v v) -5 1) PI)) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))
2.0s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
1.8s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (- U U*) (* (* n (/ l Om)) (/ l Om))))))

rewrite45.0s (3.8%)

Algorithm
115×rewrite-expression-head
Calls

438 calls:

7.4s
(* (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))))
2.8s
(* (* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1)))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k)))
2.4s
(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.4s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
1.4s
(* (* (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1)))) (/ (cbrt (/ 2 t)) (cbrt (tan k))))
Rules
94433×times-frac
43337×add-sqr-sqrt
41002×*-un-lft-identity
40337×add-cube-cbrt
25555×cbrt-prod
8038×add-exp-log
7459×sqrt-prod
7218×associate-*r*
5689×add-cbrt-cube
4032×div-inv
3990×div-exp
2887×cbrt-undiv
2358×prod-exp
1807×cbrt-unprod
1799×prod-diff
1575×pow1
1323×associate-*l*
1168×associate-/l*
824×associate-/r/
759×associate-/r*
647×unswap-sqr
523×pow-prod-down
516×associate-*r/
515×add-log-exp
509×sqrt-div
468×unpow-prod-up
438×expm1-log1p-u log1p-expm1-u insert-posit16
419×frac-times
375×unpow-prod-down
308×cbrt-div
290×associate-*l/
235×flip3-- flip--
227×distribute-rgt-in distribute-lft-in tan-quot
225×sqrt-pow1
201×1-exp flip-+ flip3-+
192×difference-of-squares
173×distribute-lft-out--
138×*-commutative
136×distribute-rgt-neg-in
134×pow-prod-up
132×distribute-lft-neg-in
130×exp-sum
128×pow-exp
125×distribute-lft-out
121×sqr-pow
117×sub-neg
112×pow1/2
110×fma-neg
107×frac-sub
106×frac-2neg clear-num pow-to-exp
75×pow1/3
74×pow-plus
72×swap-sqr
69×cos-sum
64×rem-sqrt-square
63×associate-/l/
62×pow-sqr
56×pow-unpow fma-def
47×fma-udef
42×associate--l+
35×unpow2
24×rec-exp pow2 associate--r+
22×pow-sub diff-log
20×sum-log pow-pow
14×+-commutative
12×neg-mul-1
10×cube-unmult frac-add
8×associate-+l+
6×distribute-rgt-out--
5×pow-flip inv-pow div-sub
4×associate-+r+ neg-log hypot-udef
3×remove-posit16 cos-diff distribute-rgt-out
2×neg-sub0 associate--l- sqrt-unprod sqr-sin asin-acos hypot-def acos-asin un-div-inv associate--r- sin-mult
1×distribute-lft1-in sub-div rem-square-sqrt log-pow

regimes19.7s (1.6%)

Accuracy

Total 47.5b remaining (26.4%)

Threshold costs 4.6b (2.6%)

9.4b12.7%Toniolo and Linder, Equation (13)
9.4b-6.5%Henrywood and Agarwal, Equation (13)
6.9b30.3%Henrywood and Agarwal, Equation (3)
5.3b77.3%Toniolo and Linder, Equation (7)
4.0b-17.2%Maksimov and Kolovsky, Equation (3)

localize5.9s (0.5%)

bsearch4.5s (0.4%)

end1.0ms (0.0%)