Details

simplify5.4m (44.1%)

sample4.6m (37.5%)

Algorithm
56×intervals
16×halfpoints
Results
56.8s66153×body1280valid
35.4s17568×body2560valid
22.0s42037×body640valid
12.0s12312×body10240exit
8.3s94002×body80valid
7.2s20900×body320valid
5.3s64209×body80nan
2.2s10791×body160valid
1.9s47328×pre80true
684.0ms704×body1280nan
554.0ms664×body640nan
462.0ms506×body5120valid
193.0ms387×body320nan
42.0ms191×body160nan

prune1.0m (8.2%)

series38.2s (5.2%)

Calls

369 calls:

2.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
1.9s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1)))
557.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
544.0ms
(+ (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (- (/ (/ (sin eps) (cos eps)) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (/ (sin x) (cos x))))
471.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))

rewrite24.6s (3.4%)

Algorithm
116×rewrite-expression-head
Calls

369 calls:

2.1s
(- (+ (+ (/ 1/2 n) (+ 1 (/ -1/6 (* n n)))) (log n)) 1)
1.6s
(* (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)) (- (exp (* a eps)) 1))
1.5s
(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
619.0ms
(* (cbrt (- (+ (* -1/2 (* x x)) -1) x)) (cbrt (- (+ (* -1/2 (* x x)) -1) x)))
595.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2))))
Rules
7479×*-un-lft-identity
7236×times-frac
5641×add-sqr-sqrt
3667×add-cube-cbrt
2213×sqrt-prod
1485×distribute-lft-out
1300×add-exp-log
1136×pow1
1102×add-cbrt-cube
946×associate-*l*
703×difference-of-squares
666×cbrt-prod
648×add-log-exp
534×associate-*r*
494×distribute-lft-out--
465×div-inv
453×associate-/r/
407×associate-/r*
371×swap-sqr
363×insert-posit16
358×flip-+ flip3-+
341×associate-/l*
314×prod-exp
297×log-prod
289×div-exp
272×cbrt-unprod
248×pow-prod-down
235×associate-*l/
212×unswap-sqr
192×cbrt-undiv flip3-- flip--
134×unpow-prod-down
126×pow-prod-up
110×frac-times
99×diff-log
93×associate-/l/
91×associate-*r/
88×sub-neg
85×sqrt-div
84×cbrt-div
83×*-commutative
80×pow-sqr
78×pow-flip sqr-pow
74×distribute-rgt-neg-in
71×sqrt-pow1
68×frac-2neg clear-num
65×pow-unpow
64×frac-add
63×pow1/2
61×difference-of-sqr-1
60×log-pow
59×sum-log
58×pow-plus
55×pow1/3
50×1-exp rec-exp
44×frac-sub
43×pow2
41×associate-+r+
34×distribute-rgt-in distribute-lft-in
33×inv-pow exp-prod rem-sqrt-square
30×+-commutative
23×rem-log-exp
22×log-div
19×un-div-inv
17×tan-quot div-sub
16×associate-+l+ associate--l+
13×difference-of-sqr--1
11×associate--l- associate--r+
10×neg-sub0 pow-exp pow-to-exp
8×neg-log
7×distribute-rgt-out--
5×pow-pow
4×associate-+l-
3×associate-+r- sin-mult sqr-sin
2×exp-diff sin-sum sub-div tan-sum exp-neg +.c-commutative cos-sum
1×quot-tan remove-posit16 diff-atan sqrt-undiv sin-cos-mult cube-unmult pow3 log-rec sqrt-unprod rem-exp-log rem-square-sqrt diff-sin diff-cos

localize4.9s (0.7%)

regimes4.4s (0.6%)

Accuracy

Total 28.3b remaining (21.7%)

Threshold costs 5.3b (4.1%)

5.2b81.1%quad2p (problem 3.2.1, positive)
5.1b81.3%quadp (p42, positive)
4.7b82.8%quadm (p42, negative)
3.7b86.7%quad2m (problem 3.2.1, negative)
2.9b0%expq3 (problem 3.4.2)

bsearch1.9s (0.3%)

end1.0ms (0.0%)