Details

simplify5.2m (41.6%)

sample4.4m (35.1%)

Algorithm
56×intervals
16×halfpoints
Results
49.8s66726×body1280valid
30.9s17286×body2560valid
17.7s41720×body640valid
10.2s12640×body10240exit
8.9s93988×body80valid
6.6s21158×body320valid
5.6s63102×body80nan
2.6s10865×body160valid
1.4s47396×pre80true
632.0ms708×body1280nan
587.0ms342×body320nan
343.0ms477×body5120valid
329.0ms625×body640nan
34.0ms194×body160nan

prune1.6m (13.1%)

series47.6s (6.4%)

Calls

380 calls:

1.3s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (/ (* (* (* (sin eps) (sin x)) (* (sin eps) (sin x))) (* (sin eps) (sin x))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps)))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
1.3s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
750.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
727.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
650.0ms
(log (sqrt (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))))

rewrite14.4s (1.9%)

Algorithm
119×rewrite-expression-head
Calls

380 calls:

412.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
408.0ms
(- x (sin x))
346.0ms
(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N)))) (cbrt (/ (+ 1.0 N) (sqrt N))))))
276.0ms
(log (sqrt (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))))
260.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
Rules
12807×*-un-lft-identity
11557×times-frac
10490×add-sqr-sqrt
7858×add-cube-cbrt
5226×prod-diff
2109×sqrt-prod
1692×pow1
1388×distribute-lft-out
1350×log-prod
1178×difference-of-squares
1161×add-exp-log
1109×distribute-lft-out--
1003×add-cbrt-cube
730×associate-+l+
690×unpow-prod-down
633×add-log-exp
595×div-inv
537×cbrt-prod
515×associate-/r/
502×fma-neg
454×pow-prod-down
447×associate-/l*
369×expm1-log1p-u log1p-expm1-u
365×distribute-rgt-in distribute-lft-in
324×prod-exp
322×distribute-rgt-neg-in
321×exp-sum
302×cbrt-unprod
284×associate-*l*
280×associate-/r*
262×flip3-- flip--
252×pow-prod-up
249×distribute-lft-neg-in
241×associate-*r*
231×sqr-pow
216×log-pow
214×flip-+ flip3-+
187×div-exp
164×sqrt-div
141×sqrt-pow1
126×pow-sqr
112×diff-log
111×sub-neg
105×cbrt-undiv
102×swap-sqr
98×tan-quot
96×unswap-sqr exp-prod
92×fma-def
89×associate-*l/
83×associate-*r/
82×pow-plus
81×neg-mul-1
76×frac-times
72×pow-unpow
66×pow1/3
63×*-commutative
61×pow1/2 log-div
58×pow2
57×associate-/l/
55×frac-2neg clear-num
38×cbrt-div
37×fma-udef
35×div-sub
34×associate-+r+
30×rem-sqrt-square
29×rem-log-exp
28×1-exp rec-exp
25×unpow-prod-up
23×sum-log
21×cube-unmult
20×associate--l+
17×+-commutative
15×frac-sub complex-mul-def
13×exp-diff neg-sub0
12×pow-exp associate--l- distribute-neg-in
11×sin-mult pow-pow frac-add
10×associate-+r- neg-log
9×cos-mult pow-to-exp
7×cos-sum
6×pow3 exp-to-pow
5×sub-div associate--r+ distribute-rgt-out-- rem-exp-log associate-+l- hypot-def difference-cubes
4×pow-flip *.c-commutative distribute-frac-neg sqrt-unprod inv-pow pow-sub
3×sin-sum +.c-commutative un-div-inv cube-div
2×rem-cube-cbrt associate-*l*.c sin-cos-mult complex-def-add tan-sum e-exp-1 complex-add-def
1×diff-atan cube-prod unpow3 sqr-sin distribute-lft-in.c rem-square-sqrt distribute-rgt-in.c diff-sin associate-+l+.c rem-cbrt-cube cube-mult diff-cos

regimes6.4s (0.9%)

Accuracy

Total 46.5b remaining (23.4%)

Threshold costs 6.2b (3.1%)

13.9b37.4%expax (section 3.5)
6.6b31.5%expq3 (problem 3.4.2)
4.6b83.7%quad2p (problem 3.2.1, positive)
4.6b83.6%quad2m (problem 3.2.1, negative)
4.6b83.7%quadm (p42, negative)

localize5.2s (0.7%)

bsearch2.5s (0.3%)

end1.0ms (0.0%)