Details

simplify3.5m (50.3%)

sample1.9m (27.6%)

Algorithm
56×intervals
16×halfpoints
Results
24.7s66933×body1280valid
17.5s17712×body2560valid
8.6s41464×body640valid
4.0s12323×body10240exit
3.0s94375×body80valid
2.6s20581×body320valid
1.7s63482×body80nan
861.0ms10511×body160valid
545.0ms47393×pre80true
322.0ms683×body1280nan
219.0ms679×body640nan
139.0ms431×body5120valid
64.0ms346×body320nan
23.0ms212×body160nan

series38.9s (9.4%)

Calls

388 calls:

649.0ms
(/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
498.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
486.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
486.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
482.0ms
(/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

prune31.0s (7.5%)

rewrite16.0s (3.9%)

Algorithm
123×rewrite-expression-head
Calls

388 calls:

2.1s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
392.0ms
(* (/ (sqrt (sqrt 1.0)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (pow (sqrt (sqrt 1.0)) 3) (* (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
359.0ms
(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
350.0ms
(/ 1 (* 2.0 (* (/ 1 (* 4.0 c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))))
266.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
Rules
4578×*-un-lft-identity
4369×add-sqr-sqrt
3939×times-frac
2548×add-cube-cbrt
2153×sqrt-prod
1364×add-exp-log
1003×add-cbrt-cube
816×associate-*r*
722×pow1
702×distribute-lft-out
699×unpow-prod-down
680×difference-of-squares
665×add-log-exp
505×associate-*l*
467×associate-/l*
379×distribute-lft-out--
378×prod-exp
375×cbrt-prod
357×log-prod
335×associate-/r*
321×sqr-pow
297×cube-prod
282×div-exp
257×unswap-sqr
250×flip-+ flip3-+
236×associate-/r/
220×flip-- flip3--
216×cbrt-unprod
198×associate-*l/
182×swap-sqr
177×cbrt-undiv
164×div-inv
154×associate-*r/
145×sqrt-div
142×associate-+l+
130×unpow2
126×cbrt-div
124×frac-times
114×pow-prod-down
109×pow-unpow
96×diff-log
94×sub-neg
89×pow1/3
78×log-pow
77×associate-/l/
76×*-commutative
73×clear-num frac-2neg
72×distribute-rgt-neg-in
70×pow-to-exp pow-exp
66×sum-log
55×frac-add
54×associate-+r+
51×distribute-lft-neg-in
50×exp-prod
49×distribute-rgt-in distribute-lft-in
41×sqrt-pow1
39×exp-sum
36×log-div
33×pow1/2
32×+-commutative
31×neg-mul-1
28×pow-pow div-sub 1-exp rec-exp
23×associate--l+ tan-quot
22×rem-sqrt-square pow-prod-up
21×frac-sub
16×difference-cubes pow-sqr rem-log-exp
15×unpow3 associate-+l-
13×complex-mul-def
12×neg-sub0
11×sum-cubes cube-mult pow-plus
10×associate--r+
sqrt-undiv pow2
distribute-rgt-out-- associate-+r- pow-flip
associate--l-
inv-pow distribute-frac-neg neg-log
cube-div rem-cube-cbrt *.c-commutative distribute-rgt-out
exp-diff +.c-commutative quot-tan
cos-sum sub0-neg rem-exp-log sqrt-unprod cube-unmult sin-cos-mult complex-add-def exp-neg sqr-cos sin-mult tan-sum frac-2neg.c sin-sum
un-div-inv distribute-lft1-in associate-+l+.c distribute-rgt1-in diff-atan associate-*l*.c diff-cos count-2 rem-square-sqrt sub-div cos-mult rem-cbrt-cube exp-to-pow diff-sin

regimes2.7s (0.6%)

Accuracy

Total 24.5b remaining (19.5%)

Threshold costs 5.8b (4.6%)

5.5b76.9%quadm (p42, negative)
4.7b83.4%quadp (p42, positive)
3.8b60.8%expq3 (problem 3.4.2)
1.7b92.9%quad2p (problem 3.2.1, positive)
1.6b91%2nthrt (problem 3.4.6)

localize1.8s (0.4%)

bsearch1.4s (0.3%)

end1.0ms (0.0%)