Details

simplify5.3m (44.2%)

sample4.5m (38.1%)

Algorithm
56×intervals
16×halfpoints
Results
54.0s66864×body1280valid
31.1s17297×body2560valid
18.9s42188×body640valid
10.6s12596×body10240exit
7.8s94158×body80valid
5.7s20297×body320valid
5.1s62879×body80nan
1.9s10749×body160valid
1.6s47456×pre80true
1.2s726×body1280nan
454.0ms678×body640nan
415.0ms442×body5120valid
168.0ms368×body320nan
37.0ms187×body160nan

series46.9s (6.6%)

Calls

391 calls:

961.0ms
(cbrt (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))
716.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
695.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
654.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt (* (cbrt x) (cbrt x))) (* (cbrt x) (cbrt (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
620.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

prune46.9s (6.6%)

rewrite23.2s (3.2%)

Algorithm
124×rewrite-expression-head
Calls

391 calls:

3.2s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
653.0ms
(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
536.0ms
(* (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))) (cbrt (+ (* 0.3333333333333333 x) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))))))
520.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
406.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
5294×*-un-lft-identity
4952×times-frac
4400×add-sqr-sqrt
2995×add-cube-cbrt
1242×sqrt-prod
1216×add-exp-log
923×add-cbrt-cube
864×distribute-lft-out
798×associate-*r*
733×pow1
701×add-log-exp
564×unpow-prod-down
492×difference-of-squares
486×cbrt-prod
482×associate-*l*
408×associate-/l*
370×distribute-lft-out--
330×associate-/r*
297×prod-exp
277×unswap-sqr
274×div-inv
244×div-exp
243×flip-+ flip3-+
242×flip3-- flip--
238×distribute-rgt-neg-in
237×associate-*l/
223×associate-/r/
220×sqr-pow
198×distribute-lft-neg-in
182×log-prod
167×cbrt-unprod
165×cbrt-undiv
153×unpow2
135×cbrt-div
124×swap-sqr
119×sqrt-div
116×log-pow
112×sub-neg frac-times
108×diff-log
105×associate-*r/
103×exp-sum
96×pow-prod-down
95×associate-/l/
87×cube-prod
82×pow1/3
80×frac-add sqrt-pow1
76×pow-exp
75×*-commutative
74×pow-to-exp
72×frac-2neg clear-num
69×sum-log
63×neg-mul-1
60×pow1/2
58×pow-unpow
52×exp-prod
41×log-div
39×distribute-rgt-in distribute-lft-in
37×div-sub
36×pow-prod-up
33×+-commutative
32×tan-quot
28×rem-sqrt-square pow-sqr
24×associate-+l+
23×frac-sub
21×associate--l+
18×rem-log-exp
17×associate-+r+ associate--r+
14×neg-sub0
13×complex-mul-def
12×pow-plus pow2
11×exp-diff associate--l-
10×1-exp distribute-frac-neg rec-exp
9×associate-+l-
8×unpow3 cube-mult neg-log
7×distribute-rgt-out--
6×pow-pow pow-flip
5×sqrt-unprod
4×sub0-neg inv-pow distribute-neg-in *.c-commutative
3×cube-div rem-exp-log associate-+r- sub-div +.c-commutative
2×rem-cube-cbrt sin-cos-mult distribute-lft-neg-out associate--r- exp-neg complex-add-def rem-square-sqrt tan-sum cos-sum frac-2neg.c sin-sum
1×associate-+l+.c diff-atan diff-cos unsub-neg associate-*l*.c sin-mult cos-mult exp-to-pow diff-sin rem-cbrt-cube

regimes4.0s (0.6%)

Accuracy

Total 17.6b remaining (16.1%)

Threshold costs 7.8b (7.2%)

3.2b88%quadp (p42, positive)
1.7b80.7%2nthrt (problem 3.4.6)
1.3b94.5%quad2p (problem 3.2.1, positive)
1.3b94.7%quadm (p42, negative)
1.3b94.7%quad2m (problem 3.2.1, negative)

localize3.4s (0.5%)

bsearch2.1s (0.3%)

end1.0ms (0.0%)