Details

simplify5.0m (44.4%)

sample4.3m (38.0%)

Algorithm
56×intervals
16×halfpoints
Results
52.4s66337×body1280valid
31.5s17453×body2560valid
19.8s41851×body640valid
11.7s12323×body10240exit
10.0s94230×body80valid
5.8s20939×body320valid
4.6s63738×body80nan
2.6s10848×body160valid
1.8s47324×pre80true
749.0ms422×body5120valid
677.0ms670×body1280nan
461.0ms666×body640nan
134.0ms382×body320nan
66.0ms195×body160nan

prune50.7s (7.4%)

series40.4s (5.9%)

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))
1.7s
(- (* (/ (+ (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))
685.0ms
(cbrt x)
610.0ms
(* (cbrt (* 1/12 x)) (cbrt (* 1/12 x)))
530.0ms
(/ (+ (* (cbrt (+ x 1)) x) (* (+ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (* -2 (cbrt (+ x 1)))) (+ x -1))) (* (* (cbrt (+ x 1)) x) (+ x -1)))

rewrite16.7s (2.5%)

Algorithm
119×rewrite-expression-head
Calls

384 calls:

1.3s
(- (+ (+ (/ 1/2 n) (+ 1 (/ -1/6 (* n n)))) (log n)) 1)
870.0ms
(* (* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x)) (- (+ (* -1/2 (* x x)) -1) x))
557.0ms
(* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x))
546.0ms
(+ (- (/ (/ 1 (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ 2 x)) (/ 1 (- x 1)))
507.0ms
(cbrt (* (* (- (+ (* -1/2 (* x x)) -1) x) (- (+ (* -1/2 (* x x)) -1) x)) (- (+ (* -1/2 (* x x)) -1) x)))
Rules
3333×*-un-lft-identity
3193×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×difference-of-squares prod-exp
438×distribute-lft-out
427×cbrt-unprod
424×cbrt-prod
377×insert-posit16
332×distribute-lft-out--
287×associate-*l/
261×flip3-- associate-/l* flip--
251×log-prod
241×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
100×sub-neg diff-log
99×associate-/l/
93×pow-sqr
88×*-commutative
80×sqr-pow
68×pow-unpow
67×pow-plus
66×sum-log pow1/3
65×log-pow
63×sqrt-pow1
62×pow1/2
50×frac-2neg clear-num
47×distribute-rgt-in distribute-lft-in
46×pow2
45×rem-sqrt-square
37×associate--l+
35×log-div
34×+-commutative
31×distribute-rgt-out
26×difference-of-sqr-1
23×rem-log-exp
20×associate--r+
19×frac-sub exp-prod
18×div-sub
17×associate-+r+ 1-exp rec-exp
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×exp-diff sin-sum associate-+r- exp-to-pow
2×quot-tan sin-cos-mult exp-sum pow3 tan-sum exp-neg +.c-commutative cos-sum e-exp-1
1×remove-posit16 diff-atan frac-2neg.c rem-square-sqrt diff-sin rem-cbrt-cube diff-cos distribute-rgt1-in

regimes5.3s (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%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)