Details

simplify7.8m (51.4%)

sample5.1m (33.3%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66560×body1280valid
38.6s16921×body2560valid
29.5s42914×body640valid
14.1s12495×body10240exit
10.9s93760×body80valid
9.5s20587×body320valid
6.6s63444×body80nan
3.3s10821×body160valid
2.5s47318×pre80true
751.0ms684×body1280nan
537.0ms663×body640nan
462.0ms404×body5120valid
200.0ms358×body320nan
54.0ms190×body160nan

prune1.4m (9.1%)

series34.9s (3.8%)

Calls

338 calls:

866.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
699.0ms
(fma (- (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b))))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (* (cbrt (sqrt (fma (* -4 a) c (* b b)))) (cbrt (sqrt (fma (* -4 a) c (* b b)))))))
549.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
530.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
441.0ms
(sqrt (fma (* a c) -4 (* b b)))

rewrite9.5s (1.0%)

Algorithm
115×rewrite-expression-head
Calls

338 calls:

555.0ms
(+ (+ (+ (/ 1/2 n) (+ 1 (log n))) (/ -1/6 (* n n))) -1)
328.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
185.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
182.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin eps) (/ (* (cos x) (cos eps)) (sin x))))) (/ (sin x) (cos x)))
178.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
Rules
11964×times-frac
11629×*-un-lft-identity
11191×add-sqr-sqrt
7978×add-cube-cbrt
5241×prod-diff
2815×sqrt-prod
1658×pow1
1424×difference-of-squares
1190×add-exp-log
978×add-cbrt-cube
932×distribute-lft-out
777×div-inv
734×unpow-prod-down
713×distribute-lft-out--
534×add-log-exp
522×fma-neg
453×pow-prod-up
441×associate-/r*
440×associate-/r/
423×associate-/l*
379×associate-*l*
337×log1p-expm1-u
332×expm1-log1p-u
331×insert-posit16
313×associate-*r*
312×pow-prod-down
287×div-exp
266×prod-exp
252×sqr-pow
248×associate-+l+
210×cbrt-unprod
202×pow-sqr
195×flip3-- flip--
189×cbrt-undiv
183×cbrt-prod
178×distribute-rgt-neg-in
168×pow-plus
152×flip-+ flip3-+ unswap-sqr
145×sqrt-div
140×log-prod swap-sqr
126×distribute-lft-neg-in
123×pow2
110×fma-def
92×exp-prod
85×log-pow
82×frac-2neg clear-num
78×pow-flip
77×sqrt-pow1
74×diff-log
72×sub-neg
65×pow-unpow
61×exp-sum
60×*-commutative
59×pow1/2
50×1-exp rec-exp
48×associate-/l/
46×inv-pow
42×neg-mul-1
39×tan-quot
33×sum-log
30×associate-*r/
29×rem-sqrt-square
28×associate-*l/
27×pow1/3
25×div-sub
23×associate--l+
20×+-commutative fma-udef
19×frac-times
18×pow-exp pow-to-exp
16×distribute-rgt-in distribute-lft-in
13×expm1-udef difference-of-sqr-1
12×pow-div frac-sub cbrt-div frac-add
10×hypot-def rem-log-exp log-div
8×neg-sub0 associate--l- associate--r+
7×expm1-log1p
6×neg-log sin-mult
5×exp-diff pow-pow un-div-inv distribute-rgt-out-- rem-exp-log
4×associate-+r+ associate-+l- log1p-def
3×cube-unmult log1p-udef sqr-sin exp-to-pow
2×cos-mult sin-sum sqrt-undiv sqrt-unprod sub-div +.c-commutative tan-sum exp-neg rem-square-sqrt cos-sum
1×diff-atan frac-2neg.c sin-cos-mult log1p-expm1 diff-sin +-inverses diff-cos expm1-def difference-of-sqr--1

localize5.0s (0.5%)

regimes4.3s (0.5%)

Accuracy

Total 22.1b remaining (14.9%)

Threshold costs 3.0b (2%)

5.0b81.7%quadm (p42, negative)
4.2b84.6%quad2p (problem 3.2.1, positive)
3.9b-22.7%expq3 (problem 3.4.2)
3.0b88%quad2m (problem 3.2.1, negative)
1.8b85%2nthrt (problem 3.4.6)

bsearch3.2s (0.3%)

end1.0ms (0.0%)