Details

sample4.5m (43.6%)

Algorithm
56×intervals
16×halfpoints
Results
51.5s67101×body1280valid
34.2s17627×body2560valid
19.2s41943×body640valid
11.1s12665×body10240exit
7.9s93568×body80valid
6.4s20624×body320valid
5.7s63583×body80nan
1.7s10562×body160valid
1.1s47456×pre80true
736.0ms425×body5120valid
640.0ms677×body1280nan
403.0ms699×body640nan
114.0ms349×body320nan
34.0ms172×body160nan

simplify3.3m (31.6%)

series1.1m (10.9%)

Calls

398 calls:

2.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
2.5s
(- (* (cos x) (* (+ (tan x) (tan eps)) (+ (pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3) 1))) (* (- 1 (pow (* (tan x) (tan eps)) 3)) (* (sin x) (+ (* (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) (- (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 1)) 1))))
2.0s
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.8s
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.5s
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

prune48.4s (7.8%)

rewrite28.5s (4.6%)

Algorithm
122×rewrite-expression-head
Calls

398 calls:

5.2s
(- (* (cos x) (* (+ (tan x) (tan eps)) (+ (pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3) 1))) (* (- 1 (pow (* (tan x) (tan eps)) 3)) (* (sin x) (+ (* (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) (- (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 1)) 1))))
2.7s
(- (- (+ (+ (/ 0.5 n) 1.0) (* (log n) 1.0)) (/ 0.16666666666666669 (* n n))) 1.0)
684.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
439.0ms
(* (* (- x 1.0) x) (+ x 1.0))
425.0ms
(* (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))) (sqrt (- (/ 1.0 (+ x 1.0)) (/ 1.0 x))))
Rules
3944×*-un-lft-identity
3661×add-sqr-sqrt
2678×times-frac
2097×add-cube-cbrt
1317×add-exp-log
1102×sqrt-prod
982×add-cbrt-cube
819×pow1
735×associate-*r*
697×add-log-exp
586×associate-*l*
506×distribute-lft-out
497×unpow-prod-down
485×difference-of-squares
483×distribute-lft-out--
403×log-prod
357×prod-exp
348×associate-*r/
318×associate-/l*
281×flip-- flip3--
280×cbrt-prod
276×flip-+ flip3-+
272×unswap-sqr
271×associate-/r*
225×div-exp
219×associate-*l/
211×frac-times
208×sqr-pow cbrt-unprod
177×frac-sub
166×associate-/r/
157×div-inv
155×sqrt-div
149×swap-sqr
148×cbrt-undiv
127×tan-quot
126×pow-prod-down
121×sqrt-pow1
120×cube-prod
117×diff-log
113×log-pow
109×sub-neg
94×pow1/2
90×unpow2
89×*-commutative
87×associate-/l/
84×pow-exp
81×cbrt-div
80×pow-unpow
74×pow-to-exp
67×associate-+l+ distribute-rgt-neg-in
64×log-div
62×clear-num frac-2neg
54×distribute-rgt-in distribute-lft-in
52×sum-log
48×pow1/3 exp-sum
41×pow-prod-up
38×associate--l+
37×rem-sqrt-square exp-prod
34×rem-log-exp
32×frac-add
31×associate--r+
27×pow-sqr +-commutative
25×unpow-prod-up
24×cube-div 1-exp
23×div-sub
21×unpow3 cube-mult rec-exp
20×pow-pow
15×rem-cube-cbrt
14×exp-diff neg-sub0 sum-cubes
13×associate--l- complex-mul-def associate-+r+
11×pow-flip neg-log
10×pow-plus
pow2
sqrt-unprod
associate-+l-
sin-sum inv-pow rem-square-sqrt exp-to-pow
un-div-inv rem-exp-log distribute-neg-in *.c-commutative pow-sub
associate-+r- +.c-commutative
cos-sum sin-cos-mult e-exp-1 exp-neg complex-add-def sin-mult associate--r- rem-cbrt-cube tan-sum
pow3 associate-+l+.c diff-atan diff-cos unsub-neg associate-*l*.c frac-2neg.c diff-sin

regimes4.2s (0.7%)

Accuracy

Total 27.3b remaining (21.5%)

Threshold costs 5.7b (4.5%)

4.5b83.3%quad2p (problem 3.2.1, positive)
4.3b84.5%quadp (p42, positive)
4.0b85.9%quadm (p42, negative)
4.0b85.9%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)

localize3.5s (0.6%)

bsearch2.1s (0.3%)

end1.0ms (0.0%)