Details

sample5.1m (45.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67113×body1280valid
39.6s17237×body2560valid
26.6s42016×body640valid
15.5s12757×body10240exit
12.9s93998×body80valid
9.9s20566×body320valid
7.4s62518×body80nan
3.2s10871×body160valid
2.1s47509×pre80true
1.1s708×body640nan
760.0ms647×body1280nan
439.0ms438×body5120valid
208.0ms362×body320nan
53.0ms187×body160nan

simplify4.2m (37.2%)

prune54.1s (8.0%)

series39.7s (5.8%)

Calls

354 calls:

1.8s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b))))))
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.2s
(+ (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) 1) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps))) (tan x)))
625.0ms
(+ (log (/ 1 (sqrt (exp (pow x (/ 1 n)))))) (- (pow (+ x 1) (/ 1 n)) (log (sqrt (exp (pow x (/ 1 n)))))))
570.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite13.2s (1.9%)

Algorithm
113×rewrite-expression-head
Calls

354 calls:

783.0ms
(* (- (exp (* a eps)) 1) (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (+ (* eps b) (* (* 1/2 (* eps b)) (* eps b)))))
418.0ms
(/ (* x (+ 1/27 (* (* (* x 1/45) x) (* (* (* x 1/45) x) (* (* x 1/45) x))))) (+ (* 1/3 1/3) (- (* (* x (* x 1/45)) (* x (* x 1/45))) (* 1/3 (* x (* x 1/45))))))
374.0ms
(- (- (* -2/3 (* (* eps eps) eps)) (* eps 2)) (* 2/5 (pow eps 5)))
367.0ms
(+ (* (* (* (* x a) (* x a)) (* x a)) 1/6) (* (* x a) (* (* x a) 1/2)))
343.0ms
(* (* (* (* x a) (* x a)) (* x a)) 1/6)
Rules
4664×*-un-lft-identity
3682×add-sqr-sqrt
3632×times-frac
2302×add-cube-cbrt
1896×sqrt-prod
1304×add-exp-log
1181×add-cbrt-cube
1159×pow1
906×distribute-lft-out
584×add-log-exp
492×associate-*l*
453×difference-of-squares
443×associate-*r*
398×prod-exp
390×associate-/l*
377×cbrt-unprod
366×pow-prod-down
347×insert-posit16
336×log-prod
335×distribute-lft-out--
282×cbrt-prod
249×associate-/r*
217×div-exp
208×div-inv
207×flip-+ flip3-+
182×swap-sqr
178×associate-/r/
177×associate-*l/
172×flip3-- flip--
165×cbrt-undiv
163×tan-quot
162×unswap-sqr
155×frac-times
130×sqrt-div
116×associate-*r/
115×unpow-prod-down
93×log-pow
89×sub-neg diff-log
86×*-commutative
81×associate-/l/
65×pow-unpow
63×sqrt-pow1
59×sqr-pow pow1/2
58×frac-2neg clear-num
57×pow-prod-up frac-add
55×associate-+l+
49×exp-prod
46×pow1/3 log-div
41×pow-sqr
39×sum-log
37×cbrt-div
31×associate-+r+ difference-of-sqr-1 rem-sqrt-square
28×pow-plus rem-log-exp
27×associate--l+
26×distribute-rgt-in distribute-lft-in
24×+-commutative
23×frac-sub 1-exp div-sub
19×rec-exp pow2
17×pow-flip
15×associate--r+
13×exp-sum
9×exp-diff associate--l- distribute-rgt-neg-in inv-pow
8×pow-exp pow-to-exp
6×distribute-rgt-out--
5×neg-sub0 sqrt-unprod pow-pow
4×sin-mult sub-div associate-+l-
3×sin-sum associate-+r- sqr-sin pow-div
2×cube-unmult exp-neg pow3 neg-log +.c-commutative rem-exp-log rem-square-sqrt cos-sum tan-sum e-exp-1
1×remove-posit16 diff-atan sqrt-undiv frac-2neg.c sin-cos-mult sub0-neg distribute-frac-neg un-div-inv exp-to-pow diff-sin rem-cbrt-cube diff-cos

localize4.7s (0.7%)

regimes4.1s (0.6%)

Accuracy

Total 37.8b remaining (29.4%)

Threshold costs 4.7b (3.7%)

13.6b36.9%expax (section 3.5)
4.8b82.9%quadm (p42, negative)
4.6b83.4%quadp (p42, positive)
4.6b83.5%quad2p (problem 3.2.1, positive)
2.8b0%expq3 (problem 3.4.2)

bsearch2.0s (0.3%)

end2.0ms (0.0%)