Details

sample4.5m (62.4%)

Algorithm
56×intervals
16×halfpoints
Results
51.9s66831×body1280valid
31.4s17441×body2560valid
19.5s42443×body640valid
12.3s12938×body10240exit
9.8s93740×body80valid
6.1s20678×body320valid
5.2s63451×body80nan
2.4s47351×pre80true
2.0s10509×body160valid
518.0ms700×body1280nan
427.0ms684×body640nan
288.0ms449×body5120valid
113.0ms340×body320nan
37.0ms200×body160nan

series56.6s (13.1%)

Calls

411 calls:

1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
984.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
984.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
957.0ms
(log (exp (- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))))
788.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

prune56.2s (13.0%)

rewrite21.7s (5.0%)

Algorithm
124×rewrite-expression-head
Calls

411 calls:

1.3s
(* (sqrt (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))) (* (sqrt (* (/ (fabs (cbrt (+ (exp x) (exp (- x))))) (* (sqrt (sqrt 2.0)) 1)) (/ (sqrt (cbrt (+ (exp x) (exp (- x))))) (sqrt (sqrt 2.0))))) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
506.0ms
(- (/ (+ (tan x) (tan eps)) (log (exp (- 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))
482.0ms
(+ (- (exp x) 2.0) (exp (- x)))
452.0ms
(* (sqrt (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))) (* (sqrt (/ (sqrt (+ (exp x) (exp (- x)))) (sqrt 2.0))) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
425.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
5890×*-un-lft-identity
5387×add-sqr-sqrt
5103×times-frac
3011×add-cube-cbrt
2305×sqrt-prod
1332×add-exp-log
985×add-cbrt-cube
960×difference-of-squares
837×distribute-lft-out
793×associate-*r*
752×add-log-exp
727×pow1
706×unpow-prod-down
646×distribute-lft-out--
632×associate-*l*
524×cbrt-prod
456×associate-/l*
390×associate-/r*
364×sqr-pow
320×log-prod
314×prod-exp
291×div-exp
283×associate-/r/
275×flip-- flip3--
272×unswap-sqr
244×associate-*l/
239×div-inv
211×flip-+ flip3-+
181×cbrt-undiv
178×cbrt-unprod
167×swap-sqr
164×unpow2
155×cbrt-div
151×sqrt-div
140×frac-times
129×pow-unpow
126×sub-neg
118×log-pow
117×exp-prod diff-log
114×associate-*r/
113×cube-prod
100×pow-prod-down
97×sqrt-pow1
91×associate-/l/
85×pow-to-exp pow-exp distribute-rgt-neg-in
77×clear-num frac-2neg
73×*-commutative
66×pow1/2 pow1/3
59×frac-add
53×sum-log
47×distribute-rgt-in distribute-lft-in
44×exp-sum
43×rem-sqrt-square
41×log-div
40×1-exp rec-exp
39×frac-sub
33×associate-+l+
31×+-commutative
30×pow-prod-up
27×distribute-lft-neg-in div-sub
24×pow-sqr complex-mul-def
23×exp-to-pow
22×tan-quot
21×rem-log-exp
20×associate--l+
17×neg-sub0
15×rem-exp-log
14×exp-diff pow-pow
13×associate--l- pow-flip sin-mult cos-mult
12×neg-log
11×associate--r+
10×inv-pow
9×unpow3 cube-mult pow-plus neg-mul-1 associate-+l- pow2
8×cube-div
7×sub-div
6×difference-cubes *.c-commutative
5×difference-of-sqr-1
4×+.c-commutative complex-add-def
3×rem-cube-cbrt sqrt-undiv sqrt-unprod distribute-rgt-out-- associate-+r+ rem-square-sqrt
2×associate-+l+.c exp-neg associate-*l*.c cos-sum tan-sum sin-sum
1×un-div-inv diff-atan sin-cos-mult diff-cos distribute-frac-neg rem-cbrt-cube frac-2neg.c diff-sin

simplify17.3s (4.0%)

regimes4.8s (1.1%)

Accuracy

Total 27.3b remaining (11.8%)

Threshold costs 6.6b (2.8%)

4.5b84.1%quadm (p42, negative)
4.2b84.6%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)
2.2b91.1%quad2p (problem 3.2.1, positive)
2.0b79.3%2cos (problem 3.3.5)

localize4.4s (1.0%)

bsearch2.1s (0.5%)

end1.0ms (0.0%)