Details

simplify7.8m (52.2%)

sample5.1m (34.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66560×body1280valid
38.8s16921×body2560valid
27.3s42914×body640valid
13.6s12495×body10240exit
12.8s93760×body80valid
8.9s20587×body320valid
6.8s63444×body80nan
4.1s10821×body160valid
2.0s47318×pre80true
689.0ms684×body1280nan
482.0ms663×body640nan
432.0ms404×body5120valid
167.0ms358×body320nan
52.0ms190×body160nan

prune52.9s (5.9%)

series38.0s (4.3%)

Calls

365 calls:

1.2s
(/ (/ (- (* (* 2 (+ 2 (exp x))) (* 2 (+ 2 (exp x)))) (* (* (exp x) (+ (exp x) (+ (exp (* 3 x)) -8))) (* (exp x) (+ (exp x) (+ (exp (* 3 x)) -8))))) (- (* 2 (+ 2 (exp x))) (* (exp x) (+ (exp x) (+ (exp (* 3 x)) -8))))) (* (exp x) (+ 4 (* (exp x) (+ (exp x) 2)))))
946.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
516.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
496.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
490.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite17.5s (2.0%)

Algorithm
116×rewrite-expression-head
Calls

365 calls:

1.6s
(- (+ (+ (+ (/ 1/2 n) (log n)) (/ -1/6 (* n n))) 1) 1)
1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* eps (* (* (* eps a) (* eps a)) a)) 1/6) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
911.0ms
(* (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (sqrt (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
531.0ms
(/ (+ (* 2 (+ 2 (exp x))) (* (exp x) (+ (exp x) (+ (exp (* 3 x)) -8)))) (* (exp x) (+ 4 (* (exp x) (+ (exp x) 2)))))
474.0ms
(- (tan (+ x eps)) (tan x))
Rules
5155×*-un-lft-identity
4055×times-frac
4046×add-sqr-sqrt
2884×sqrt-prod
2457×add-cube-cbrt
1883×pow1
1125×add-exp-log
1033×add-cbrt-cube
961×distribute-lft-out
653×add-log-exp
584×difference-of-squares
473×associate-*r*
457×pow-prod-down
435×pow-prod-up
432×distribute-lft-out--
379×associate-/l*
374×associate-*l*
358×insert-posit16
316×associate-*r/
306×prod-exp
301×cbrt-prod
300×associate-/r*
295×div-inv
292×cbrt-unprod
282×flip-+ flip3-+
236×sqrt-div
200×pow-sqr
198×flip3-- flip--
184×associate-/r/
175×div-exp
169×swap-sqr
166×unpow-prod-down
162×pow-plus
146×log-prod
142×unswap-sqr
137×cbrt-undiv
129×frac-times sqrt-pow1
120×associate-*l/
114×pow2
104×frac-sub sqr-pow
100×sub-neg
96×diff-log
95×exp-prod
89×log-pow
84×frac-add
79×pow1/2
78×pow-unpow *-commutative
66×frac-2neg clear-num
64×associate-/l/
61×sum-log
53×pow-flip
51×pow1/3
47×cbrt-div
46×distribute-rgt-in distribute-lft-in
40×difference-of-sqr-1
38×rem-sqrt-square
35×+-commutative
29×tan-quot
27×inv-pow log-div
23×1-exp rec-exp
22×associate-+l+
19×pow-div
18×associate--l+
17×associate--r+ rem-log-exp
16×div-sub
11×distribute-rgt-neg-in
9×pow-exp pow-to-exp
7×associate--l-
6×neg-sub0 pow-pow
5×sin-sum associate-+r+ difference-of-sqr--1 associate-+l- distribute-rgt-out distribute-rgt-out-- distribute-rgt1-in
4×exp-diff exp-sum neg-log sin-mult
3×sqrt-unprod sub-div sqr-sin exp-to-pow rem-exp-log rem-square-sqrt
2×sqrt-undiv sin-cos-mult cube-unmult exp-neg cos-sum tan-sum +.c-commutative
1×diff-atan frac-2neg.c pow3 un-div-inv diff-sin diff-cos associate--r-

localize4.7s (0.5%)

regimes4.6s (0.5%)

Accuracy

Total 25.2b remaining (18.5%)

Threshold costs 4.1b (3%)

5.1b81.6%quadm (p42, negative)
4.3b84.1%quadp (p42, positive)
4.2b84.7%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)
3.0b88.3%quad2m (problem 3.2.1, negative)

bsearch2.0s (0.2%)

end1.0ms (0.0%)