Details

sample4.4m (41.8%)

Algorithm
56×intervals
16×halfpoints
Results
49.7s66832×body1280valid
32.1s17421×body2560valid
19.5s41742×body640valid
10.6s12653×body10240exit
9.1s93899×body80valid
6.0s21068×body320valid
5.1s63893×body80nan
2.2s47209×pre80true
2.0s10867×body160valid
508.0ms664×body1280nan
401.0ms707×body640nan
347.0ms455×body5120valid
115.0ms388×body320nan
111.0ms208×body160nan

simplify2.9m (27.3%)

series1.4m (13.5%)

Calls

378 calls:

37.7s
(log (exp (* (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))))))))
825.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))))
798.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
741.0ms
(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
660.0ms
(- (/ (/ x (+ (tan x) x)) (- x (tan x))) (/ (sin x) (* (+ x (tan x)) (- x (tan x)))))

prune1.4m (13.1%)

rewrite16.3s (2.6%)

Algorithm
120×rewrite-expression-head
Calls

378 calls:

632.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ 1.0 x))))) (sqrt (/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt x) (sqrt (+ 1.0 x)))))))
432.0ms
(- (/ (sin x) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (sin x))
361.0ms
(+ (/ 1.0 (- x 1.0)) (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)))
281.0ms
(/ (/ (/ x (/ 1.0 x)) 1.0) (/ (+ (+ (/ (* -1/2 (/ x (/ 1.0 x))) 1.0) (* 1.0 x)) (log 1.0)) 1/2))
272.0ms
(* (/ (sin y) 2.0) (+ (* (pow x 5) 1/60) (+ (* 1/3 (pow x 3)) (+ x x))))
Rules
18120×times-frac
12280×*-un-lft-identity
10079×add-sqr-sqrt
8013×add-cube-cbrt
2523×sqrt-prod
1826×distribute-lft-out
1727×add-exp-log
1100×add-cbrt-cube
1082×pow1
840×associate-/l*
831×difference-of-squares
702×div-inv
656×add-log-exp
639×associate-*r*
617×div-exp
607×distribute-lft-out--
530×associate-*l*
487×log-pow
455×associate-/r*
396×associate-/r/
376×prod-exp
372×log-prod
350×unpow-prod-down
284×cbrt-undiv
275×flip3-- flip--
228×cbrt-prod
198×cbrt-unprod
180×flip-+ flip3-+
170×unswap-sqr
162×sqr-pow
152×distribute-rgt-neg-in
142×distribute-lft-neg-in
140×sqrt-div
130×cube-prod
110×sub-neg
106×associate-*l/
103×pow-prod-down
102×associate-*r/ diff-log
93×associate-+r+
89×1-exp rec-exp
84×frac-2neg clear-num
82×pow-unpow
79×associate-/l/
70×swap-sqr
66×frac-times *-commutative
62×frac-add
58×sqrt-pow1 pow1/2
51×exp-prod log-div
50×unpow-prod-up sum-log
43×pow-exp
38×pow-to-exp
37×distribute-rgt-in distribute-lft-in
35×exp-sum
29×associate-+l+ +-commutative
28×frac-sub rem-sqrt-square
27×pow1/3
25×div-sub rem-log-exp
24×pow-pow
21×cbrt-div
19×pow-prod-up cube-mult
18×neg-mul-1
17×unpow3
15×complex-mul-def
14×tan-quot
11×exp-diff pow-sqr
8×neg-sub0 distribute-rgt-out-- pow-sub
7×pow-flip sin-sum associate--l+ inv-pow
6×associate-+r- sqrt-unprod associate--l- cube-div
5×distribute-frac-neg associate--r+ distribute-neg-frac rem-exp-log
4×*.c-commutative pow2 pow-plus sub-div e-exp-1
3×quot-tan rem-cube-cbrt neg-log exp-to-pow +.c-commutative associate-+l- rem-square-sqrt
2×associate-*l*.c sin-mult un-div-inv tan-sum exp-neg unpow2 complex-add-def cos-sum rem-cbrt-cube
1×diff-atan distribute-lft1-in pow-div sub0-neg diff-sin associate-+l+.c diff-cos distribute-rgt-out

regimes5.6s (0.9%)

Accuracy

Total 26.7b remaining (20.9%)

Threshold costs 8.6b (6.7%)

4.8b83.2%quadp (p42, positive)
4.8b83.1%quad2p (problem 3.2.1, positive)
3.7b87.1%quad2m (problem 3.2.1, negative)
3.2b88.9%quadm (p42, negative)
1.7b80.9%2nthrt (problem 3.4.6)

localize4.5s (0.7%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)