Details

simplify6.0m (46.2%)

sample4.5m (34.6%)

Algorithm
56×intervals
16×halfpoints
Results
52.7s66823×body1280valid
30.6s16913×body2560valid
19.1s42623×body640valid
9.8s12526×body10240exit
8.2s93843×body80valid
6.7s20586×body320valid
5.3s63900×body80nan
2.6s10767×body160valid
1.4s47359×pre80true
886.0ms649×body1280nan
785.0ms683×body640nan
351.0ms458×body5120valid
133.0ms348×body320nan
31.0ms192×body160nan

prune1.3m (9.7%)

series46.6s (6.0%)

Calls

367 calls:

2.1s
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
848.0ms
(cbrt (cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))))
718.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
632.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
626.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite17.5s (2.3%)

Algorithm
121×rewrite-expression-head
Calls

367 calls:

934.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
477.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))
459.0ms
(* (/ 1.0 (pow n 2)) (+ (/ (* (- (log x)) -1/3) x) (/ -2/3 (/ x (- (log x))))))
435.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
280.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
Rules
13839×times-frac
11853×*-un-lft-identity
11297×add-sqr-sqrt
9306×add-cube-cbrt
6037×prod-diff
1963×unpow-prod-down
1670×sqrt-prod
1373×add-exp-log
1366×distribute-rgt-in distribute-lft-in
1177×distribute-rgt-neg-in
1165×pow1
1162×distribute-lft-neg-in
1017×add-cbrt-cube
827×difference-of-squares
763×div-inv
706×associate-/l*
678×distribute-lft-out
613×sqr-pow
603×distribute-lft-out--
569×add-log-exp
563×associate-*l*
534×log-pow
491×associate-*r*
445×cube-prod
432×fma-neg
430×cbrt-prod
398×unpow2
388×associate-/r/
372×associate-/r*
356×log1p-expm1-u
355×expm1-log1p-u
352×prod-exp
332×div-exp
315×neg-mul-1
247×associate-+l+
231×flip-- flip3--
207×cbrt-undiv
197×cbrt-unprod
178×unswap-sqr
164×flip-+ flip3-+
150×sqrt-pow1
127×fma-def
111×pow-unpow
107×pow-prod-down
96×pow-exp
95×sub-neg log-prod
90×pow1/2
89×pow-to-exp
88×diff-log
84×sqrt-div
81×unpow3 cube-mult
80×cbrt-div
78×frac-2neg swap-sqr clear-num
76×associate-*r/
68×*-commutative
63×associate-*l/
61×pow-prod-up
60×associate-/l/
47×frac-times
45×exp-prod
42×associate--l+ tan-quot
40×pow1/3
38×exp-sum
37×fma-udef
35×1-exp
33×div-sub
29×pow-sqr
28×rem-sqrt-square
26×rec-exp
23×log-div
22×sum-log
21×pow-pow
15×frac-add +-commutative
14×neg-sub0
13×cube-div complex-mul-def frac-sub
11×rem-cube-cbrt rem-log-exp
10×associate--r+
8×sqrt-unprod
7×difference-cubes un-div-inv associate--l- pow2 pow-flip pow-plus associate-+l-
6×neg-log
5×inv-pow associate--r- distribute-frac-neg
4×*.c-commutative
3×exp-neg +.c-commutative rem-square-sqrt distribute-rgt-out-- sin-sum
2×cos-sum exp-diff sin-cos-mult unpow1/3 complex-add-def quot-tan sin-mult tan-sum rem-cbrt-cube expm1-udef
1×associate-+l+.c rem-exp-log log1p-udef associate-+r- diff-atan log1p-expm1 sub-div diff-cos expm1-log1p unsub-neg associate-*l*.c distribute-rgt-neg-out frac-2neg.c sqrt-undiv diff-sin log-rec

regimes3.6s (0.5%)

Accuracy

Total 23.0b remaining (13.9%)

Threshold costs 6.7b (4%)

4.8b45.8%expq3 (problem 3.4.2)
4.7b83.6%quad2p (problem 3.2.1, positive)
3.1b89.2%quadp (p42, positive)
1.4b83.8%2nthrt (problem 3.4.6)
1.2b95.1%quad2m (problem 3.2.1, negative)

localize3.5s (0.5%)

bsearch2.8s (0.4%)

end1.0ms (0.0%)