Details

sample2.2m (37.7%)

Algorithm
61×intervals
Results
36.2s252816×body80valid
23.8s162291×body80nan
21.3s29330×body1280valid
11.1s8826×body2560valid
10.5s20086×body640valid
6.6s3343×body5120valid
3.6s9824×body320valid
2.3s9023×body160valid
866.0ms861×body10240exit
313.0ms606×body1280nan
246.0ms589×body640nan
169.0ms8256×pre80true
118.0ms354×body320nan
44.0ms191×body160nan

series1.8m (31.3%)

Calls

434 calls:

4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(/ (sqrt (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

prune1.0m (17.4%)

rewrite17.8s (5.1%)

Algorithm
116×rewrite-expression-head
Calls

434 calls:

1.3s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
652.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
650.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
426.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
38191×add-exp-log
26565×prod-exp
12316×pow-exp
10958×div-exp
5933×add-sqr-sqrt
5759×times-frac
5633×pow-to-exp
5109×*-un-lft-identity
3904×add-cube-cbrt
2909×add-cbrt-cube
2094×cbrt-prod
2027×sqrt-prod
1368×cbrt-unprod
1334×rec-exp 1-exp
1232×pow1
1185×associate-*r*
1011×associate-*l*
1008×unpow-prod-down
661×cbrt-undiv
529×prod-diff
516×difference-of-squares
503×add-log-exp
485×associate-/l*
443×associate-*r/
438×expm1-log1p-u
434×log1p-expm1-u
423×distribute-lft-out--
411×pow-unpow
409×pow-prod-down
396×frac-times
387×associate-*l/
366×distribute-rgt-neg-in
359×unswap-sqr
312×sqr-pow
308×distribute-lft-neg-in
288×distribute-lft-out
281×div-inv
263×exp-prod
255×associate-/r*
246×sqrt-div
179×flip3-- flip--
176×distribute-rgt-in distribute-lft-in
146×*-commutative
133×flip-+ flip3-+
122×associate-/r/
114×cube-prod
109×tan-quot
100×sqrt-pow1
86×frac-2neg clear-num
80×pow1/3
63×pow1/2
59×pow-pow
58×fma-def
56×rem-sqrt-square
55×fma-neg
52×sub-neg
46×cbrt-div
44×div-sub
42×associate--l+
38×associate-/l/ fma-udef
36×neg-mul-1
35×swap-sqr
32×frac-sub
31×pow-prod-up
27×unpow2 cos-sum
26×neg-sub0
24×log-pow
22×associate--r+
19×exp-diff pow-neg pow-sub
18×sum-log
17×pow-plus pow-sqr
16×+-commutative
15×diff-log
14×hypot-def
9×un-div-inv pow2
8×associate-+r- frac-add distribute-neg-frac
7×rem-exp-log unsub-neg pow-flip
6×log-prod
5×inv-pow distribute-frac-neg
4×cube-div asin-acos log1p-udef associate-+r+ log1p-expm1 unpow3 cube-mult acos-asin neg-log
3×difference-cubes rem-cbrt-cube expm1-udef
2×associate--l- pow3 sin-sum expm1-log1p hypot-udef associate--r- rem-log-exp
1×rem-cube-cbrt sqrt-unprod exp-neg cos-diff associate-+l+ rem-square-sqrt mul0 distribute-rgt-neg-out exp-to-pow

simplify12.5s (3.6%)

Algorithm
176×egg-herbie

regimes10.0s (2.9%)

Accuracy

Total 57.3b remaining (28.6%)

Threshold costs 4.2b (2.1%)

9.5b-1.9%Toniolo and Linder, Equation (13)
9.0b40.3%Henrywood and Agarwal, Equation (3)
8.0b0%Given's Rotation SVD example
7.2b10.5%Toniolo and Linder, Equation (10+)
6.1b6.8%Henrywood and Agarwal, Equation (12)

bsearch5.0s (1.4%)

localize2.3s (0.7%)

end0.0ms (0.0%)