Details

sample4.4m (44.3%)

Algorithm
56×intervals
16×halfpoints
Results
48.9s67398×body1280valid
32.7s17079×body2560valid
18.8s42063×body640valid
11.5s12817×body10240exit
9.5s93914×body80valid
6.1s20796×body320valid
4.3s62743×body80nan
2.4s10416×body160valid
1.6s47460×pre80true
1.1s670×body1280nan
479.0ms709×body640nan
281.0ms469×body5120valid
163.0ms386×body320nan
82.0ms184×body160nan

simplify3.3m (33.3%)

prune51.3s (8.6%)

series49.9s (8.4%)

Calls

392 calls:

2.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
894.0ms
(* (sqrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (+ (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (log x)) (* x (pow n 2)))))
775.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
721.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
658.0ms
(cbrt x)

rewrite22.5s (3.8%)

Algorithm
121×rewrite-expression-head
Calls

392 calls:

961.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))
875.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (- (log x))) (* x (pow n 2)))))
806.0ms
(* (sqrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (+ (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (log x)) (* x (pow n 2)))))
471.0ms
(* (cbrt (+ (/ (pow eps 2) (pow 1.0 2)) eps)) (cbrt (+ (/ (pow eps 2) (pow 1.0 2)) eps)))
428.0ms
(* (sqrt (/ (sqrt (+ (exp x) (exp (- x)))) 1)) (* (sqrt (/ (sqrt (+ (exp x) (exp (- x)))) 2.0)) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
Rules
5788×times-frac
5375×*-un-lft-identity
5107×add-sqr-sqrt
3520×add-cube-cbrt
2072×sqrt-prod
1484×add-exp-log
1101×add-cbrt-cube
838×associate-*l*
686×associate-*r*
678×pow1
663×add-log-exp
616×unpow-prod-down
577×distribute-lft-out
553×difference-of-squares
523×associate-/l*
412×prod-exp
407×associate-/r*
385×distribute-lft-out--
374×cbrt-prod
323×div-exp
283×cbrt-div
280×sqr-pow
276×unswap-sqr
248×distribute-rgt-neg-in
246×flip3-- flip--
230×cbrt-unprod
229×cube-prod
222×div-inv
220×cbrt-undiv
210×distribute-lft-neg-in
189×pow-unpow
178×flip-+ flip3-+
170×frac-times
146×associate-*l/ associate-/r/
134×associate-*r/
118×frac-sub
116×log-prod
107×sqrt-div
106×unpow2
104×log-pow
96×pow-prod-down
94×diff-log exp-prod
93×sub-neg pow-exp
91×frac-add
88×pow-to-exp
79×frac-2neg *-commutative clear-num
71×associate-/l/
70×neg-mul-1
66×swap-sqr
65×sqrt-pow1
64×pow1/3
55×pow1/2
54×sum-log
40×unpow3 cube-mult
38×rem-sqrt-square
37×distribute-rgt-in distribute-lft-in
35×1-exp rec-exp
34×+-commutative
28×tan-quot
26×exp-sum
25×pow-flip div-sub
23×pow-pow
19×associate--l+
18×log-div
17×associate-+l+
15×pow-prod-up
14×pow-div associate--r+
13×pow-sqr complex-mul-def
12×rem-cube-cbrt rem-log-exp
10×neg-sub0
8×cube-div associate--l-
7×difference-cubes un-div-inv pow2 pow-plus
6×exp-diff inv-pow neg-log associate-+l-
5×sqrt-unprod sin-sum
4×sin-mult rem-cbrt-cube *.c-commutative
3×associate-+r+ rem-exp-log exp-neg distribute-rgt-out-- +.c-commutative
2×cos-sum sin-cos-mult complex-add-def cos-mult tan-sum frac-2neg.c
1×unpow1/3 associate-+l+.c diff-atan sub-div diff-cos rem-square-sqrt associate-*l*.c sqrt-undiv exp-to-pow diff-sin

regimes3.6s (0.6%)

Accuracy

Total 22.2b remaining (20.1%)

Threshold costs 8.0b (7.2%)

4.6b83.7%quadp (p42, positive)
3.8b86.2%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)
1.6b81.6%2nthrt (problem 3.4.6)
1.1b95.4%quadm (p42, negative)

localize3.5s (0.6%)

bsearch2.3s (0.4%)

end1.0ms (0.0%)