Details

sample4.3m (35.4%)

Algorithm
56×intervals
16×halfpoints
Results
51.5s66657×body1280valid
32.7s17375×body2560valid
16.5s41976×body640valid
9.9s12961×body10240exit
8.7s93695×body80valid
5.9s62578×body80nan
5.8s20892×body320valid
2.1s11039×body160valid
1.2s47500×pre80true
530.0ms670×body1280nan
338.0ms615×body640nan
295.0ms472×body5120valid
109.0ms347×body320nan
91.0ms173×body160nan

simplify4.3m (34.7%)

prune2.0m (16.1%)

series58.5s (7.9%)

Calls

436 calls:

826.0ms
(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))
822.0ms
(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a))
776.0ms
(log (cbrt (- (pow 1.0 3) (pow x 3))))
627.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
626.0ms
(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite29.5s (4.0%)

Algorithm
126×rewrite-expression-head
Calls

436 calls:

2.1s
(- (+ (- 1.0 (+ (* 1.0 (* -1 (log n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
1.9s
(/ (- (pow (* (* (pow x 4) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)) 3) (pow (pow x 2) 3)) (* (+ (+ (* (* (* (pow x 4) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)) (* (* (pow x 4) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2))) (pow x 4)) (* (* (* (pow x 4) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)) (pow x 2))) (- (* (pow x 2) (+ (* x 1/6) 1/2)) x)))
1.8s
(/ (/ 1 (/ (/ 1 1) (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* c a)))) a)))) a)
813.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
455.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
Rules
71972×times-frac
35788×add-sqr-sqrt
35623×*-un-lft-identity
27288×add-cube-cbrt
4110×difference-of-squares
3877×associate-/l*
3723×distribute-lft-out--
2372×sqrt-prod
1843×div-inv
1636×add-exp-log
1621×distribute-rgt-neg-in
1143×cbrt-prod
1059×add-cbrt-cube
844×pow1
790×add-log-exp
739×unpow-prod-down
547×div-exp
528×log-prod
520×associate-*l* associate-*r*
470×cube-prod
465×associate-/r/
437×distribute-lft-out
398×sqr-pow
393×flip-- flip3--
332×associate-/r*
331×associate-*l/
326×prod-exp
311×frac-times
282×flip-+ flip3-+
263×unswap-sqr
215×associate-*r/
209×cbrt-undiv
191×cbrt-unprod
188×frac-sub
183×sqrt-pow1
165×swap-sqr
158×associate-/l/
145×pow-prod-down
144×exp-prod
134×pow-unpow
128×diff-log
125×sub-neg
123×exp-neg neg-sub0
122×cbrt-div
117×sqrt-div
112×exp-diff
108×1-exp
93×log-pow
92×pow1/3
91×pow1/2
84×frac-add
81×*-commutative
80×associate-+r+
79×pow-exp
77×pow-to-exp
76×rec-exp
72×unpow2
70×frac-2neg clear-num
64×pow-prod-up
58×sum-log
54×log-div
52×pow-sqr
51×associate-+l+
42×rem-log-exp
40×rem-sqrt-square
38×distribute-rgt-in distribute-lft-in
33×pow-pow
31×+-commutative
30×tan-quot
27×exp-sum
26×distribute-lft-neg-in div-sub
24×complex-mul-def
22×difference-cubes
21×unpow3 cube-mult exp-to-pow
20×un-div-inv
19×associate--l+
16×pow-flip
15×cube-div associate--l- pow-plus associate--r+
14×pow2 cos-mult
12×neg-log
10×rem-cube-cbrt neg-mul-1 associate-+l-
inv-pow difference-of-sqr-1
sqrt-unprod
rem-exp-log *.c-commutative distribute-neg-frac
rem-cbrt-cube
distribute-lft-neg-out associate-+r- distribute-rgt-out-- +.c-commutative complex-add-def rem-square-sqrt
pow-neg associate-+l+.c sub-div pow-sub cos-sum sin-mult tan-sum frac-2neg.c associate-*l*.c sin-sum log-rec
sin-cos-mult sqrt-pow2 diff-atan diff-cos diff-sin

regimes5.1s (0.7%)

Accuracy

Total 23.9b remaining (7.9%)

Threshold costs 7.3b (2.4%)

5.1b40.1%expq3 (problem 3.4.2)
3.0b89.5%quadm (p42, negative)
2.8b89.5%quad2p (problem 3.2.1, positive)
2.4b91.1%quad2m (problem 3.2.1, negative)
1.7b83.3%2cos (problem 3.3.5)

localize4.6s (0.6%)

bsearch3.5s (0.5%)

end1.0ms (0.0%)