Details

simplify5.2m (42.4%)

sample4.9m (40.5%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66337×body1280valid
38.8s17453×body2560valid
25.6s41851×body640valid
13.1s94230×body80valid
12.5s12323×body10240exit
9.2s20939×body320valid
7.2s63738×body80nan
2.7s10848×body160valid
1.8s47324×pre80true
825.0ms670×body1280nan
550.0ms666×body640nan
463.0ms422×body5120valid
170.0ms382×body320nan
53.0ms195×body160nan

prune54.4s (7.5%)

series40.5s (5.5%)

Calls

384 calls:

2.0s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
1.9s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
517.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
495.0ms
(/ (+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1))) (* (* (cbrt (+ x 1)) x) (+ x -1)))
475.0ms
(- (/ 1 x) (/ 1 (tan x)))

rewrite17.4s (2.4%)

Algorithm
119×rewrite-expression-head
Calls

384 calls:

1.3s
(- (+ (+ (/ 1/2 n) (+ 1 (/ -1/6 (* n n)))) (log n)) 1)
971.0ms
(* (* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x)) (- (+ (* -1/2 (* x x)) -1) x))
613.0ms
(cbrt (* (* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x)) (- (+ (* -1/2 (* x x)) -1) x)))
582.0ms
(+ (- (/ (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ 2 x)) (/ 1 (- x 1)))
571.0ms
(* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x))
Rules
3331×*-un-lft-identity
3183×add-sqr-sqrt
2354×times-frac
1813×add-cube-cbrt
1502×pow1
1357×add-exp-log
1235×add-cbrt-cube
838×sqrt-prod
682×add-log-exp
469×pow-prod-down
464×associate-*r*
463×associate-*l*
453×prod-exp
448×difference-of-squares
442×distribute-lft-out
427×cbrt-unprod
424×cbrt-prod
377×insert-posit16
328×distribute-lft-out--
287×associate-*l/
261×associate-/l*
259×flip3-- flip--
250×log-prod
243×flip-+ flip3-+
213×frac-times
207×swap-sqr
199×associate-/r*
191×cbrt-div
184×div-exp
166×associate-*r/
157×unswap-sqr
153×div-inv
148×cbrt-undiv
142×tan-quot
140×associate-/r/
138×unpow-prod-down
127×pow-prod-up
125×frac-add
112×sqrt-div
99×associate-/l/
97×sub-neg diff-log
93×pow-sqr
88×*-commutative
80×sqr-pow
69×sum-log
68×pow-unpow
67×pow-plus
66×pow1/3
63×sqrt-pow1
62×pow1/2 log-pow
50×frac-2neg clear-num
47×distribute-rgt-in distribute-lft-in
46×pow2
45×rem-sqrt-square
36×associate--l+ +-commutative
34×log-div
31×distribute-rgt-out
24×difference-of-sqr-1
23×rem-log-exp
20×associate--r+
19×frac-sub
18×associate-+r+ div-sub
17×1-exp rec-exp
16×exp-prod
15×pow-flip
13×pow-exp
12×distribute-rgt-neg-in
11×associate-+l+ associate--l- pow-to-exp
9×inv-pow
8×neg-sub0
6×sin-mult pow-pow
5×neg-log sqr-sin associate-+l-
4×sqrt-unprod rem-exp-log associate--r-
3×sin-sum associate-+r- exp-to-pow
2×quot-tan exp-diff sin-cos-mult pow3 tan-sum exp-neg +.c-commutative cos-sum e-exp-1
1×remove-posit16 diff-atan frac-2neg.c exp-sum rem-square-sqrt diff-sin rem-cbrt-cube diff-cos distribute-rgt1-in

regimes5.8s (0.8%)

Accuracy

Total 26.3b remaining (20.4%)

Threshold costs 5.7b (4.4%)

5.2b81.5%quad2m (problem 3.2.1, negative)
4.4b84.4%quad2p (problem 3.2.1, positive)
4.1b84.9%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)
2.2b92.2%quadm (p42, negative)

localize4.7s (0.7%)

bsearch2.0s (0.3%)

end1.0ms (0.0%)