Details

sample4.6m (41.6%)

Algorithm
56×intervals
16×halfpoints
Results
52.0s66982×body1280valid
34.5s17531×body2560valid
18.9s42033×body640valid
11.1s12945×body10240exit
7.4s93711×body80valid
7.0s20423×body320valid
6.2s63822×body80nan
2.4s10943×body160valid
1.8s47413×pre80true
830.0ms635×body640nan
559.0ms638×body1280nan
273.0ms408×body5120valid
199.0ms363×body320nan
80.0ms211×body160nan

simplify3.9m (35.6%)

series1.0m (9.3%)

Calls

408 calls:

1.7s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.6s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.6s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.6s
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

prune52.5s (8.0%)

rewrite24.2s (3.7%)

Algorithm
125×rewrite-expression-head
Calls

408 calls:

2.9s
(- (- (+ (+ (/ 0.5 n) 1.0) (* 1.0 (log n))) (/ 0.16666666666666669 (* n n))) 1.0)
1.0s
(* (* (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))) (/ (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x)))
435.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
360.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
317.0ms
(* (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
Rules
4367×*-un-lft-identity
4343×add-sqr-sqrt
3653×times-frac
2500×add-cube-cbrt
1326×add-exp-log
985×add-cbrt-cube
838×sqrt-prod
725×add-log-exp
703×pow1
696×unpow-prod-down
691×difference-of-squares
684×associate-*r*
630×associate-*l*
493×distribute-lft-out--
485×distribute-lft-out
404×associate-/r*
355×associate-/l*
344×flip-- flip3--
332×prod-exp
307×unswap-sqr
305×sqr-pow
282×cbrt-prod
272×cube-prod div-exp
268×associate-/r/
252×flip-+ flip3-+
231×associate-*l/
204×pow-unpow
200×div-inv
193×cbrt-div
185×log-prod
182×cbrt-undiv
180×associate-*r/
174×cbrt-unprod
155×exp-prod
138×frac-times
127×log-pow
126×frac-add
124×sub-neg
122×sqrt-div
116×diff-log
111×unpow2
110×associate-/l/
102×pow-exp
100×pow-to-exp
94×sqrt-pow1
90×pow-prod-down
88×swap-sqr
85×exp-sum
78×frac-2neg clear-num
74×pow1/2
72×*-commutative
64×log-div
60×sum-log
55×frac-sub
52×distribute-rgt-in unpow3 distribute-lft-in cube-mult
48×pow1/3 distribute-rgt-neg-in
45×tan-quot
38×pow-pow
37×rem-sqrt-square
35×+-commutative
28×associate--l+
26×associate-+l+ div-sub
25×pow-prod-up
22×1-exp rec-exp
19×associate--r-
17×pow-sqr rem-log-exp
13×complex-mul-def neg-sub0
12×associate-+r+ associate--r+
10×cube-div rem-cube-cbrt sum-cubes
exp-diff associate--l- pow-flip
associate-+l-
neg-log
sqrt-unprod inv-pow pow2 pow-plus distribute-frac-neg
rem-exp-log exp-neg
distribute-lft-neg-out distribute-neg-in rem-cbrt-cube *.c-commutative
distribute-lft-neg-in difference-cubes un-div-inv distribute-rgt-out-- +.c-commutative rem-square-sqrt
cos-sum complex-add-def quot-tan sin-mult tan-sum sin-sum
sin-cos-mult associate-+r- associate-+l+.c diff-atan sub-div diff-cos unsub-neg associate-*l*.c neg-mul-1 frac-2neg.c diff-sin

regimes4.3s (0.7%)

Accuracy

Total 25.6b remaining (14%)

Threshold costs 6.3b (3.5%)

5.5b36.8%expq3 (problem 3.4.2)
4.4b84.9%quadp (p42, positive)
3.5b87.6%quadm (p42, negative)
3.2b88.1%quad2p (problem 3.2.1, positive)
1.4b81.2%2tan (problem 3.3.2)

localize4.2s (0.6%)

bsearch3.5s (0.5%)

end1.0ms (0.0%)