Details

prune1.9m (31.2%)

series1.6m (25.9%)

Calls

447 calls:

5.0s
(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 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.3s
(* (* (* 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*))))

sample1.5m (23.7%)

Algorithm
61×intervals
Results
16.3s252893×body80valid
16.2s29589×body1280valid
10.3s158314×body80nan
8.7s8774×body2560valid
7.5s19902×body640valid
5.7s3378×body5120valid
2.5s9973×body320valid
1.3s8891×body160valid
455.0ms773×body10240exit
156.0ms604×body1280nan
125.0ms617×body640nan
106.0ms8256×pre80true
53.0ms354×body320nan
19.0ms186×body160nan

rewrite39.2s (10.6%)

Algorithm
117×rewrite-expression-head
Calls

447 calls:

2.5s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.0s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (* (* c0 (* d d)) (/ 1 (* (* w h) (* D D)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
1.8s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
1.7s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))
853.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
Rules
39917×add-exp-log
34161×times-frac
26214×prod-exp
16611×add-sqr-sqrt
16106×*-un-lft-identity
15134×add-cube-cbrt
14872×div-exp
14675×pow-exp
8962×unpow-prod-down
7277×pow-to-exp
4423×associate-*r*
4348×cbrt-prod
3377×sqrt-prod
3014×add-cbrt-cube
2352×1-exp
1748×rec-exp
1704×sqr-pow
1601×associate-*l*
1420×pow1
1389×cbrt-unprod
747×unpow2
709×associate-/l*
603×div-inv
577×cbrt-undiv
560×add-log-exp
545×associate-*r/
465×pow-prod-down
444×unswap-sqr
441×distribute-lft-out
437×associate-/r*
416×pow-unpow
376×frac-times
362×associate-*l/
336×sqrt-div
202×flip3-- flip--
181×distribute-rgt-neg-in
178×flip-+ flip3-+
155×distribute-lft-out--
150×associate-/r/
149×exp-prod
146×*-commutative
145×sqrt-pow1
130×difference-of-squares
96×tan-quot
95×distribute-lft-neg-in
92×frac-2neg clear-num
90×pow1/2
76×distribute-rgt-in distribute-lft-in
73×sub-neg
68×rem-sqrt-square
58×pow-prod-up
56×pow1/3 pow-pow
55×cube-prod
54×log-prod
49×div-sub
41×sum-log
40×frac-sub
38×pow-sqr
36×swap-sqr
31×associate-/l/
28×+-commutative associate--l+
26×exp-sum
25×cube-div
24×cbrt-div
23×pow-plus
22×neg-sub0
21×log-pow
20×frac-add
19×pow2
18×pow-sub
17×exp-diff
16×diff-log
14×pow-flip associate-+r+
12×associate-+r-
11×rem-cube-cbrt neg-mul-1
10×cos-sum
9×unpow3 inv-pow unsub-neg cube-mult
8×pow-neg unpow-prod-up distribute-neg-frac
7×rem-exp-log
5×cos-diff rem-log-exp
4×un-div-inv acos-asin neg-log associate-+l-
3×sqrt-unprod
2×associate-+l+ rem-square-sqrt distribute-frac-neg asin-acos rem-cbrt-cube associate--r+ log-div
1×mul0

simplify14.8s (4.0%)

Algorithm
177×egg-herbie

regimes11.8s (3.2%)

Accuracy

Total 46.5b remaining (21.4%)

Threshold costs 4.8b (2.2%)

7.7b30.9%Henrywood and Agarwal, Equation (3)
7.3b23.7%Toniolo and Linder, Equation (13)
7.0b15.8%Toniolo and Linder, Equation (10+)
5.7b0%Henrywood and Agarwal, Equation (12)
5.7b76.5%Toniolo and Linder, Equation (7)

bsearch2.7s (0.7%)

localize2.6s (0.7%)

end0.0ms (0.0%)