Details

simplify12.5m (55.4%)

sample5.0m (22.1%)

Algorithm
56×intervals
16×halfpoints
Results
56.1s66750×body1280valid
34.3s16915×body2560valid
26.2s42952×body640valid
12.4s12723×body10240exit
10.4s93370×body80valid
8.8s20720×body320valid
6.8s63553×body80nan
2.6s10923×body160valid
2.4s47339×pre80true
1.1s622×body1280nan
510.0ms655×body640nan
409.0ms520×body5120valid
151.0ms358×body320nan
47.0ms187×body160nan

prune2.3m (10.1%)

series1.2m (5.2%)

Calls

413 calls:

6.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* (* 1/6 (* b (* b b))) (* eps (* eps eps))) (+ (* eps b) (* (* (* b eps) (* b eps)) 1/2)))))
1.2s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
1.1s
(log (/ (exp (pow (+ x 1.0) (/ 1.0 n))) (exp (pow x (/ 1.0 n)))))
975.0ms
(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (+ (* x x) (+ (* (tan x) (tan x)) (* x (tan x)))))
897.0ms
(- (* (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x)))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin eps) (/ (sin x) (cos eps))) (cos x))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x))))

rewrite1.1m (4.8%)

Algorithm
125×rewrite-expression-head
Calls

413 calls:

4.5s
(- (+ (- (+ 1.0 (/ 0.5 n)) (/ 0.16666666666666669 (* n n))) (* 1.0 (log n))) 1.0)
3.7s
(/ (+ (* 0.3333333333333333 0.3333333333333333) (- (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)) (* 0.3333333333333333 (* (* x x) 0.022222222222222223)))) (+ (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223))) (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333)))
3.3s
(* x (+ (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223))) (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333)))
3.2s
(/ x (/ (+ (* 0.3333333333333333 0.3333333333333333) (- (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)) (* 0.3333333333333333 (* (* x x) 0.022222222222222223)))) (+ (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223))) (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333))))
2.1s
(* (- (exp (* a eps)) 1.0) (+ (* (* 1/6 (* b (* b b))) (* eps (* eps eps))) (+ (* eps b) (* (* (* b eps) (* b eps)) 1/2))))
Rules
6051×*-un-lft-identity
5383×times-frac
5025×add-sqr-sqrt
3051×add-cube-cbrt
2399×sqrt-prod
2037×add-exp-log
1716×pow1
1701×add-cbrt-cube
998×distribute-lft-out
792×difference-of-squares
774×prod-exp
764×add-log-exp
700×associate-*r*
666×associate-*l*
588×cbrt-unprod
578×distribute-lft-out--
556×pow-prod-down
485×associate-/l*
407×div-exp
402×insert-posit16
331×associate-/r/
319×associate-/r*
301×flip-+ flip3-+
299×sqrt-div
285×cbrt-undiv
282×swap-sqr
278×div-inv
275×associate-*r/
268×associate-*l/
238×flip3-- flip--
201×frac-times
187×pow-prod-up
182×unpow-prod-down
177×unswap-sqr
164×distribute-rgt-neg-in
149×log-prod
129×distribute-lft-neg-in
116×diff-log
115×sub-neg
110×*-commutative
102×cbrt-prod
99×pow-sqr
97×associate-/l/
93×sqr-pow
81×pow-plus
77×sqrt-pow1
75×pow1/2
73×frac-2neg clear-num
67×log-pow
65×exp-prod
61×sum-log frac-sub
56×1-exp rec-exp
55×pow-unpow
51×cbrt-div frac-add
40×pow3
37×pow2 div-sub
35×distribute-rgt-in +-commutative distribute-lft-in rem-sqrt-square
31×cube-unmult
28×pow1/3 neg-mul-1 exp-to-pow log-div
26×exp-lft-cube
23×difference-cubes
22×associate--l+
17×sum-cubes
16×pow-flip tan-quot associate--r+ rem-log-exp
15×associate-+l+ pow-exp pow-to-exp
14×neg-sub0 complex-mul-def
12×associate-+r+
11×associate--l-
cos-mult sin-mult
pow-pow associate-+l- sqr-cos
distribute-neg-frac
exp-sum pow-div distribute-frac-neg neg-log inv-pow rem-exp-log
exp-diff cube-prod associate-+r- sqrt-unprod rem-square-sqrt
sin-sum *.c-commutative difference-of-sqr-1 sqr-sin +.c-commutative cos-sum
associate-*l*.c sin-cos-mult exp-neg sub-div un-div-inv complex-add-def tan-sum rem-cbrt-cube distribute-neg-in associate--r- distribute-rgt-out
remove-posit16 diff-atan distribute-rgt-out-- rem-cube-cbrt distribute-rgt-neg-out unpow3 +-inverses frac-2neg.c diff-sin associate-+l+.c cube-mult diff-cos

localize20.2s (1.5%)

regimes11.5s (0.8%)

Accuracy

Total 39.8b remaining (28.2%)

Threshold costs 6.8b (4.8%)

14.0b35%expax (section 3.5)
4.3b85.5%quadp (p42, positive)
4.1b85.8%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)
3.1b88.9%quadm (p42, negative)

bsearch2.2s (0.2%)

end1.0ms (0.0%)