Details

simplify22.7m (76.6%)

sample4.5m (15.3%)

Algorithm
56×intervals
16×halfpoints
Results
52.4s66599×body1280valid
33.4s17327×body2560valid
20.9s41902×body640valid
10.4s12868×body10240exit
9.4s93800×body80valid
6.0s64266×body80nan
6.0s21104×body320valid
2.4s10710×body160valid
1.3s47408×pre80true
819.0ms674×body640nan
607.0ms654×body1280nan
357.0ms510×body5120valid
294.0ms374×body320nan
39.0ms207×body160nan

prune53.7s (3.0%)

series52.0s (2.9%)

Calls

389 calls:

804.0ms
(/ (- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x))) (* (* (cos x) (cos eps)) (cos x)))
758.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
753.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
677.0ms
(- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x)))
641.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite28.4s (1.6%)

Algorithm
124×rewrite-expression-head
Calls

389 calls:

2.2s
(- (+ (- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n)))) (/ 0.5 n)) 1.0)
1.2s
(exp (- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2))))))
1.1s
(exp (+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))))
556.0ms
(cbrt (* (* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
513.0ms
(- (+ (/ 0.3333333333333333 (* N N)) (- (log 1.0) (log N))) (+ (/ 0.5 N) (/ 0.125 (* (pow N 2) (pow 1.0 2)))))
Rules
5773×*-un-lft-identity
5292×times-frac
4867×add-sqr-sqrt
3260×add-cube-cbrt
2957×sqrt-prod
1614×add-exp-log
1281×add-cbrt-cube
823×associate-*l*
798×distribute-lft-out
785×pow1
772×add-log-exp
742×associate-*r*
613×difference-of-squares
594×distribute-lft-out--
467×prod-exp
439×associate-/r*
436×associate-/l*
389×unpow-prod-down
360×div-exp
331×cbrt-unprod
320×cbrt-prod
271×flip-+ flip3-+ associate-*l/
269×div-inv
256×associate-/r/
254×cbrt-undiv
241×flip3-- flip--
223×unswap-sqr
180×sqr-pow
162×pow-unpow
149×sqrt-div
138×pow-prod-down
133×associate-*r/
129×associate-/l/ frac-times
127×diff-log cbrt-div
104×sum-log
103×log-prod
100×swap-sqr
96×sub-neg
88×unpow2
85×*-commutative
84×frac-add
83×frac-2neg clear-num distribute-rgt-neg-in
81×log-pow
70×pow-exp
65×pow-to-exp
62×pow1/3
60×cube-prod
51×frac-sub
46×sqrt-pow1
38×distribute-rgt-in distribute-lft-in
37×+-commutative
36×pow1/2
35×tan-quot exp-sum
31×1-exp exp-prod rec-exp
29×log-div
26×associate--l+
25×pow-flip div-sub
24×cos-mult
19×pow-pow associate-+l+ rem-sqrt-square
17×unpow3 cube-mult
16×rem-exp-log
14×pow-prod-up pow-sqr neg-sub0
13×complex-mul-def associate-+l- associate--r+
12×exp-diff
11×neg-log
10×pow-div associate-+r- associate-+r+ associate--l-
9×inv-pow
8×pow-plus
7×rem-cube-cbrt pow2 rem-log-exp
4×cube-div unpow-prod-up sin-mult *.c-commutative sin-sum
3×sin-cos-mult un-div-inv sqrt-unprod +.c-commutative complex-add-def rem-cbrt-cube sqrt-undiv
2×cos-sum pow3 exp-neg pow-sub tan-sum
1×sub0-neg difference-cubes e-exp-1 distribute-lft-in.c associate-+l+.c diff-atan distribute-rgt-in.c diff-cos distribute-frac-neg associate-*l*.c sqr-cos distribute-rgt-neg-out frac-2neg.c cube-unmult exp-to-pow diff-sin

regimes4.0s (0.2%)

Accuracy

Total 33.5b remaining (25.9%)

Threshold costs 6.0b (4.6%)

6.1b79.1%quadp (p42, positive)
5.9b82.7%quad2p (problem 3.2.1, positive)
5.5b77.1%quad2m (problem 3.2.1, negative)
5.5b77.2%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)

localize3.4s (0.2%)

bsearch2.3s (0.1%)

end0.0ms (0.0%)