Details

simplify5.1m (41.6%)

sample4.4m (35.7%)

Algorithm
56×intervals
16×halfpoints
Results
48.8s66810×body1280valid
31.2s17396×body2560valid
19.2s41741×body640valid
10.8s12737×body10240exit
8.7s93751×body80valid
7.1s21173×body320valid
5.9s63286×body80nan
2.4s10876×body160valid
1.7s47298×pre80true
573.0ms623×body1280nan
361.0ms675×body640nan
271.0ms415×body5120valid
133.0ms397×body320nan
35.0ms196×body160nan

prune1.1m (9.2%)

series53.6s (7.3%)

Calls

400 calls:

2.6s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (/ (tan x) (/ (cos eps) (sin eps))) (/ (tan x) (/ (cos eps) (sin eps)))) (/ (tan x) (/ (cos eps) (sin eps)))))) (+ (* 1 1) (+ (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))) (* 1 (/ (* (tan x) (sin eps)) (cos eps)))))) (tan x))
1.3s
(/ (- (* (exp (* a x)) (sqrt (exp (* a x)))) (* (sqrt 1.0) 1.0)) (+ (exp (* a x)) (+ 1.0 (* (sqrt 1.0) (sqrt (exp (* a x)))))))
1.2s
(* (/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps))) (/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* b eps)) 1.0)))
1.2s
(log (* (cbrt (exp (* (* x x) 0.022222222222222223))) (cbrt (exp (* (* x x) 0.022222222222222223)))))
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2)) (* eps a)) (- (exp (* b eps)) 1.0)))

rewrite31.2s (4.2%)

Algorithm
123×rewrite-expression-head
Calls

400 calls:

4.6s
(* (/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps))) (/ (- (exp (* (+ a b) eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.4s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* 1.0 (log n))) 1.0)
2.1s
(/ eps (+ (+ (* (* (* a eps) (* (* a eps) (* a eps))) 1/6) (* 1/2 (* (* a eps) (* a eps)))) (* a eps)))
1.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* a (* a a)) (* eps (* eps eps))) 1/6) (* (* (* eps a) (* eps a)) 1/2)) (* eps a)) (- (exp (* b eps)) 1.0)))
1.0s
(/ (+ (* (* eps eps) eps) (* (* (* (/ eps 1.0) (/ eps 1.0)) (* (/ eps 1.0) (/ eps 1.0))) (* (/ eps 1.0) (/ eps 1.0)))) (+ (* (* (/ eps 1.0) (/ eps 1.0)) (* (/ eps 1.0) (/ eps 1.0))) (- (* eps eps) (* (* (/ eps 1.0) (/ eps 1.0)) eps))))
Rules
4410×*-un-lft-identity
3587×times-frac
3529×add-sqr-sqrt
2445×add-cube-cbrt
1749×pow1
1699×add-exp-log
1671×add-cbrt-cube
1138×sqrt-prod
779×distribute-lft-out
728×add-log-exp
593×prod-exp
574×cbrt-unprod
542×associate-*l/
434×pow-prod-down
410×difference-of-squares
387×associate-*r*
382×associate-/l*
366×associate-/r*
353×div-exp
344×associate-*l*
339×cbrt-undiv
313×associate-/r/
310×log-prod
307×pow-prod-up
303×distribute-lft-out--
297×flip--
296×flip3--
271×frac-times
268×flip-+
267×flip3-+
257×associate-*r/
250×div-inv
235×cbrt-prod
181×frac-add pow-sqr
151×pow-plus
146×frac-sub
142×exp-prod
134×associate-/l/
129×unpow-prod-down
122×swap-sqr
116×diff-log
113×unswap-sqr
105×sub-neg
101×log-pow
95×pow2
92×distribute-rgt-neg-in
81×associate-+r+
76×sqr-pow
75×frac-2neg clear-num
73×distribute-lft-neg-in
72×*-commutative
68×sqrt-div
60×sum-log sqrt-pow1
58×exp-sum
56×pow-unpow
55×pow1/3
53×pow3
43×cbrt-div
42×pow1/2
38×+-commutative
36×log-div
33×div-sub
30×associate-+l+ rem-sqrt-square
27×tan-quot
24×neg-mul-1
23×difference-cubes
22×cube-unmult
21×distribute-rgt-in distribute-lft-in
20×rem-log-exp associate--l+
15×cube-prod
14×complex-mul-def
13×neg-sub0
12×exp-to-pow associate-+l-
11×associate--r+ sum-cubes
10×associate--l-
pow-exp pow-to-exp sqr-cos
exp-diff cos-mult 1-exp rec-exp sin-mult
neg-log pow-pow distribute-rgt-out--
associate-+r- pow-flip
distribute-frac-neg distribute-neg-frac
quot-tan exp-neg *.c-commutative un-div-inv +.c-commutative cos-sum distribute-rgt-out
associate-*l*.c sin-sum sub-div rem-exp-log complex-add-def tan-sum rem-cbrt-cube distribute-neg-in associate--r-
diff-atan unsub-neg rem-cube-cbrt distribute-rgt-neg-out cube-mult unpow3 sqrt-unprod frac-2neg.c inv-pow +-inverses rem-square-sqrt diff-sin associate-+l+.c diff-cos count-2 cos-2

regimes6.0s (0.8%)

Accuracy

Total 20.6b remaining (16.5%)

Threshold costs 7.2b (5.7%)

4.2b85.5%quad2p (problem 3.2.1, positive)
4.2b85.5%quadp (p42, positive)
2.6b90.1%quad2m (problem 3.2.1, negative)
1.3b85.4%2nthrt (problem 3.4.6)
1.1b95.6%quadm (p42, negative)

localize6.0s (0.8%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)