Details

sample4.4m (41.5%)

Algorithm
56×intervals
16×halfpoints
Results
49.0s66936×body1280valid
32.9s17492×body2560valid
21.1s42279×body640valid
10.5s12740×body10240exit
7.8s93598×body80valid
7.1s20720×body320valid
3.9s63478×body80nan
1.7s10751×body160valid
1.7s47309×pre80true
567.0ms638×body1280nan
392.0ms665×body640nan
337.0ms449×body5120valid
182.0ms330×body320nan
34.0ms182×body160nan

simplify3.8m (35.4%)

prune59.8s (9.4%)

series53.4s (8.4%)

Calls

386 calls:

1.8s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.4s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* a eps) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
1.1s
(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (pow (cbrt x) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))))
897.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite22.6s (3.5%)

Algorithm
119×rewrite-expression-head
Calls

386 calls:

2.1s
(* (/ (/ 1 (sqrt 1)) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
865.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
594.0ms
(- (/ (pow (exp x) 3) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))) (/ (pow 1.0 3) (+ (* 1.0 (+ 1.0 (exp x))) (exp (+ x x)))))
558.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
389.0ms
(* (+ (pow (sqrt (exp (* 2.0 x))) 3) (pow (sqrt 1.0) 3)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
Rules
11287×times-frac
9319×*-un-lft-identity
8953×add-sqr-sqrt
5480×sqrt-prod
5371×add-cube-cbrt
1395×add-exp-log
1377×distribute-lft-out
1264×associate-*r*
1057×cbrt-prod
1005×difference-of-squares
990×add-cbrt-cube
795×unpow-prod-down
728×associate-*l*
709×associate-/l*
694×add-log-exp
687×pow1
673×distribute-lft-out--
525×unswap-sqr
440×associate-/r*
364×sqr-pow
350×div-exp
342×prod-exp
307×div-inv
262×associate-/r/
227×cube-prod
216×flip-- flip3--
199×cbrt-undiv
195×unpow2
187×sqrt-div
185×cbrt-unprod
171×flip-+ flip3-+
145×log-prod
120×sub-neg
118×diff-log
113×pow-to-exp pow-exp
93×pow-prod-down
88×associate-*r/
87×log-pow
81×pow-unpow
75×*-commutative
73×associate-/l/
71×clear-num frac-2neg
69×tan-quot
68×frac-times
64×associate-*l/
59×sqrt-pow1
57×pow1/2
56×cbrt-div
53×exp-prod
51×pow1/3
50×1-exp sum-log
47×rec-exp swap-sqr
38×distribute-rgt-neg-in
34×rem-sqrt-square
31×distribute-rgt-in cube-mult distribute-lft-in
30×unpow3
29×log-div +-commutative
24×complex-mul-def div-sub
23×pow-pow associate--l+
22×pow-prod-up frac-sub
19×associate--r+ rem-log-exp
18×pow-sqr
16×frac-add pow-flip
15×neg-sub0
14×associate-+l+ inv-pow exp-sum
13×distribute-rgt-out--
10×associate-+l-
9×rem-exp-log associate--l- pow-plus
8×neg-log pow2 cos-mult
7×exp-diff difference-cubes
6×*.c-commutative associate-+r+
5×rem-cube-cbrt sqrt-unprod sqr-cos sin-mult
4×un-div-inv +.c-commutative complex-add-def exp-to-pow
3×sin-cos-mult associate-+r- pow-sub distribute-rgt-out pow-neg
2×associate-+l+.c exp-neg sub-div difference-of-sqr-1 rem-square-sqrt associate-*l*.c tan-sum cos-sum sin-sum
1×sqrt-pow2 sum-cubes diff-atan diff-cos +-inverses frac-2neg.c diff-sin log-rec

regimes5.5s (0.9%)

Accuracy

Total 26.6b remaining (12.4%)

Threshold costs 7.2b (3.3%)

4.7b83.3%quad2p (problem 3.2.1, positive)
4.7b83.3%quadp (p42, positive)
2.7b0%expq3 (problem 3.4.2)
1.9b92.4%quad2m (problem 3.2.1, negative)
1.9b78.8%2nthrt (problem 3.4.6)

localize4.1s (0.6%)

bsearch2.1s (0.3%)

end2.0ms (0.0%)