Details

simplify5.1m (43.8%)

sample4.5m (38.3%)

Algorithm
56×intervals
16×halfpoints
Results
51.2s66823×body1280valid
31.1s16913×body2560valid
20.7s42623×body640valid
10.5s12526×body10240exit
8.8s93843×body80valid
7.2s20586×body320valid
4.9s63900×body80nan
2.4s10767×body160valid
1.0s47359×pre80true
591.0ms649×body1280nan
518.0ms458×body5120valid
439.0ms683×body640nan
121.0ms348×body320nan
37.0ms192×body160nan

prune47.5s (6.8%)

series47.0s (6.7%)

Calls

397 calls:

606.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
584.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))
549.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
513.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (* (tan x) (tan eps))) (cbrt (* (tan x) (tan eps)))) (cbrt (* (tan x) (tan eps)))))) (tan x))
512.0ms
(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))

rewrite20.7s (3.0%)

Algorithm
123×rewrite-expression-head
Calls

397 calls:

517.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
453.0ms
(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (cbrt (+ x 1.0))))) (cbrt (cbrt (cbrt (+ x 1.0)))))) (cbrt x))
424.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
352.0ms
(log (* (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))) (sqrt (exp (cos (/ (+ (+ x eps) x) 2))))))
324.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ 1 (/ N (- 1.0 (/ 0.5 N)))))
Rules
4600×add-sqr-sqrt
4462×*-un-lft-identity
4401×times-frac
2825×add-cube-cbrt
1478×add-exp-log
1061×add-cbrt-cube
1044×sqrt-prod
810×associate-*r*
719×pow1
654×add-log-exp
619×difference-of-squares
608×unpow-prod-down
559×associate-*l*
486×associate-/l*
448×associate-/r*
443×distribute-lft-out--
413×distribute-lft-out
397×prod-exp
340×div-exp
261×unswap-sqr
253×sqr-pow
247×flip-- flip3--
240×cbrt-prod
211×associate-/r/
210×div-inv
207×cbrt-unprod
203×cbrt-undiv
186×associate-*l/
183×flip-+ flip3-+
156×unpow2
139×log-pow
133×log-prod
128×associate-*r/
121×pow-exp
118×pow-to-exp
112×sub-neg
107×cbrt-div
103×diff-log
97×frac-times
95×cube-prod
94×sqrt-pow1
92×associate-/l/ pow-prod-down
87×frac-2neg clear-num
86×distribute-rgt-neg-in
80×exp-prod
77×*-commutative
73×pow-unpow
70×swap-sqr
66×distribute-lft-neg-in
58×pow1/2
56×sqrt-div frac-add
54×distribute-rgt-in distribute-lft-in
51×pow1/3
39×neg-mul-1
37×sum-log
35×div-sub
32×tan-quot
31×pow-prod-up
28×rem-sqrt-square
25×log-div frac-sub
23×pow-sqr unpow3
22×+-commutative
21×1-exp
20×rec-exp cube-mult exp-sum
17×associate-+l+
15×neg-sub0 associate--l+ rem-log-exp
13×pow-pow complex-mul-def
12×associate--r+
11×cube-div
9×distribute-rgt-out-- distribute-frac-neg
8×pow-flip
7×pow2 pow-plus associate-+l-
6×exp-diff associate--l- inv-pow associate-+r+ neg-log
4×un-div-inv sqrt-unprod distribute-neg-in cos-mult *.c-commutative
3×rem-cube-cbrt sub0-neg rem-exp-log +.c-commutative rem-square-sqrt
2×pow-div cos-sum associate-+r- associate--r- exp-neg sub-div complex-add-def sqrt-undiv sqr-cos sin-mult tan-sum rem-cbrt-cube sin-sum
1×sin-cos-mult associate-+l+.c distribute-lft-neg-out diff-atan diff-cos unsub-neg associate-*l*.c frac-2neg.c diff-sin

regimes3.8s (0.5%)

Accuracy

Total 20.7b remaining (12%)

Threshold costs 6.8b (3.9%)

4.7b41.9%expq3 (problem 3.4.2)
3.0b87.4%expax (section 3.5)
1.6b81.5%2nthrt (problem 3.4.6)
1.2b95%quad2m (problem 3.2.1, negative)
1.2b95.9%quadp (p42, positive)

localize3.4s (0.5%)

bsearch2.9s (0.4%)

end1.0ms (0.0%)