Details

simplify8.0m (45.9%)

sample5.0m (28.5%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66849×body1280valid
41.2s17149×body2560valid
28.3s42219×body640valid
13.4s12690×body10240exit
11.8s94355×body80valid
8.4s20688×body320valid
6.5s63524×body80nan
2.6s10707×body160valid
2.3s47417×pre80true
686.0ms641×body1280nan
524.0ms476×body5120valid
463.0ms660×body640nan
203.0ms402×body320nan
82.0ms194×body160nan

prune3.6m (20.5%)

series34.4s (3.3%)

Calls

341 calls:

628.0ms
(cbrt x)
597.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) b)
551.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
491.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
490.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

rewrite8.2s (0.8%)

Algorithm
110×rewrite-expression-head
Calls

341 calls:

565.0ms
(+ (- (+ (/ 1/2 n) 1) (- (/ 1/6 (* n n)) (log n))) -1)
381.0ms
(/ (* x (fma (* 1/91125 (* (* x x) x)) (* (* x x) x) 1/27)) (+ (* 1/3 1/3) (- (* (* (* x 1/45) x) (* (* x 1/45) x)) (* 1/3 (* (* x 1/45) x)))))
167.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
165.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
136.0ms
(cbrt (* (* (* (sin x) (/ (sin eps) (cos eps))) (* (sin x) (/ (sin eps) (cos eps)))) (* (sin x) (/ (sin eps) (cos eps)))))
Rules
13643×times-frac
12467×*-un-lft-identity
11579×add-sqr-sqrt
9188×add-cube-cbrt
6427×prod-diff
3556×sqrt-prod
1548×pow1
1189×difference-of-squares
1123×add-exp-log
990×add-cbrt-cube
889×div-inv
761×distribute-lft-out--
709×distribute-lft-out
556×associate-*l*
543×fma-neg
524×add-log-exp
393×associate-/r/
385×pow-prod-up
383×distribute-rgt-neg-in
366×distribute-lft-neg-in
351×associate-/l*
340×log1p-expm1-u
336×expm1-log1p-u
335×associate-*r*
301×associate-+l+
290×cbrt-prod
275×prod-exp
268×associate-/r*
262×pow-prod-down
259×pow-plus
237×cbrt-unprod
234×div-exp
219×flip-+ flip3-+
206×flip3-- flip--
198×unpow-prod-down
176×cbrt-undiv
149×pow-sqr
136×sqrt-div
130×associate-*l/
122×neg-mul-1
110×distribute-rgt-in distribute-lft-in
108×unswap-sqr
104×frac-times fma-def
94×pow2
89×log-pow
79×diff-log
78×pow-unpow
77×associate-*r/
73×pow-flip
72×frac-2neg clear-num sub-neg
71×sqrt-pow1
68×sqr-pow
64×log-prod
63×*-commutative
56×exp-prod
55×pow1/2
46×cbrt-div
39×associate-/l/
37×1-exp rec-exp
36×associate--r+
35×rem-sqrt-square
34×pow1/3
30×sum-log
29×tan-quot
28×pow3
27×frac-add
23×inv-pow fma-udef
22×frac-sub
20×+-commutative
19×div-sub
18×hypot-def
17×associate--l+
16×pow-div difference-of-sqr-1
15×pow-pow
13×swap-sqr
12×associate--l-
10×rem-log-exp
9×neg-sub0 expm1-udef log-div
8×pow-exp
7×expm1-log1p pow-to-exp log1p-udef
5×neg-log
4×log1p-def log1p-expm1 distribute-rgt-out-- associate-+l- sin-mult
3×sub-div sqr-sin rem-cbrt-cube associate--r-
2×exp-diff sin-sum un-div-inv +.c-commutative tan-sum exp-neg cos-sum e-exp-1
1×diff-atan cos-mult frac-2neg.c sin-cos-mult cube-unmult hypot-udef rem-exp-log diff-sin diff-cos expm1-def difference-of-sqr--1

localize4.2s (0.4%)

regimes4.0s (0.4%)

Accuracy

Total 19.5b remaining (13.7%)

Threshold costs 6.4b (4.5%)

4.3b84.8%quadm (p42, negative)
4.3b84.8%quad2m (problem 3.2.1, negative)
3.2b0%expq3 (problem 3.4.2)
1.4b88.5%2nthrt (problem 3.4.6)
0.9b96.2%quad2p (problem 3.2.1, positive)

bsearch2.7s (0.3%)

end2.0ms (0.0%)