Details

simplify5.0m (42.8%)

sample4.4m (37.1%)

Algorithm
56×intervals
16×halfpoints
Results
51.3s66642×body1280valid
31.2s17576×body2560valid
22.5s42571×body640valid
11.2s13021×body10240exit
7.6s93739×body80valid
6.9s20711×body320valid
5.9s63589×body80nan
2.6s47423×pre80true
2.2s10639×body160valid
968.0ms640×body1280nan
354.0ms478×body5120valid
346.0ms646×body640nan
122.0ms366×body320nan
32.0ms172×body160nan

prune55.7s (7.9%)

series43.8s (6.2%)

Calls

383 calls:

2.9s
(- (cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))
2.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* b (* (* eps 1/6) (* (* eps b) (* eps b)))) (* eps b)) (* (* 1/2 (* eps b)) (* eps b)))))
1.8s
(pow (exp (* (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))) (cbrt (log (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))))
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))) (tan x))

rewrite31.4s (4.4%)

Algorithm
119×rewrite-expression-head
Calls

383 calls:

4.9s
(* (- (exp (* a eps)) 1) (+ (+ (* b (* (* eps 1/6) (* (* eps b) (* eps b)))) (* eps b)) (* (* 1/2 (* eps b)) (* eps b))))
2.0s
(- (+ (+ (/ 1/2 n) (+ 1 (/ -1/6 (* n n)))) (log n)) 1)
1.4s
(* (/ (+ 1/27 (* (* (* x x) (* x x)) (* (* x x) 1/91125))) (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))) (/ x (sqrt (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))))
1.2s
(cbrt (* (* (+ (+ (/ (/ 1 x) n) 1) (/ (log x) n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n))))
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* b (* (* eps 1/6) (* (* eps b) (* eps b)))) (* eps b)) (* (* 1/2 (* eps b)) (* eps b)))))
Rules
5062×*-un-lft-identity
3967×add-sqr-sqrt
3706×times-frac
2348×add-cube-cbrt
1983×sqrt-prod
1517×pow1
1477×add-exp-log
1326×add-cbrt-cube
1029×distribute-lft-out
671×add-log-exp
586×associate-*l*
558×associate-*r*
503×difference-of-squares
473×prod-exp
427×pow-prod-down
421×cbrt-unprod
375×insert-posit16
344×associate-/l*
334×distribute-lft-out--
320×tan-quot
308×log-prod
291×associate-*l/
286×cbrt-prod
283×swap-sqr
279×frac-times
248×associate-/r*
243×div-exp
230×div-inv
222×flip-+ flip3-+
209×associate-/r/
197×flip3-- flip--
196×cbrt-undiv
192×associate-*r/
188×unswap-sqr
149×pow-prod-up
111×pow-unpow
107×pow-sqr
106×*-commutative
99×unpow-prod-down
97×sqrt-div
92×sub-neg
89×cbrt-div diff-log
79×log-pow
78×associate-/l/
73×pow-plus
69×sum-log
66×exp-prod
63×frac-2neg clear-num frac-add
53×pow2
47×pow1/3
43×distribute-rgt-in sqr-pow distribute-lft-in
42×sqrt-pow1 pow1/2 log-div
41×frac-sub exp-sum
39×associate-+l+
35×+-commutative
34×difference-of-sqr-1
30×rem-sqrt-square
26×rem-log-exp
25×pow-flip 1-exp rec-exp
21×div-sub
20×pow-exp associate--l+ pow-to-exp
15×associate-+r+ distribute-rgt-neg-in
14×associate--r+
13×inv-pow
11×pow-pow
9×associate--l- sin-mult
8×neg-sub0 exp-to-pow
7×rem-exp-log
6×neg-log sqr-sin
5×exp-diff cos-mult
4×sub-div un-div-inv distribute-rgt-out--
3×sin-sum sin-cos-mult associate-+l- cos-sum
2×associate-+r- frac-2neg.c cube-unmult pow-div pow3 tan-sum exp-neg +.c-commutative
1×diff-atan sqrt-unprod rem-square-sqrt diff-sin rem-cbrt-cube diff-cos difference-of-sqr--1

regimes4.9s (0.7%)

Accuracy

Total 30.4b remaining (20%)

Threshold costs 6.3b (4.2%)

5.2b82%quadp (p42, positive)
5.0b81.6%quadm (p42, negative)
4.7b83.6%quad2m (problem 3.2.1, negative)
4.6b83.8%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)

localize4.6s (0.6%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)