Details

simplify4.7m (42.5%)

sample4.4m (39.7%)

Algorithm
56×intervals
16×halfpoints
Results
54.3s67113×body1280valid
29.6s17237×body2560valid
20.8s42016×body640valid
12.0s12757×body10240exit
8.7s93998×body80valid
5.7s20566×body320valid
4.9s62518×body80nan
3.2s10871×body160valid
1.6s47509×pre80true
1.0s647×body1280nan
786.0ms438×body5120valid
472.0ms708×body640nan
153.0ms362×body320nan
36.0ms187×body160nan

prune50.9s (7.7%)

series39.6s (6.0%)

Calls

361 calls:

1.9s
(/ (* 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))))
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.2s
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x)))
539.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
518.0ms
(* (/ (sin x) x) (/ (tan (/ x 2)) x))

rewrite15.4s (2.3%)

Algorithm
115×rewrite-expression-head
Calls

361 calls:

1.2s
(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* (* (* b eps) (* b eps)) eps)) eps)) (* (* (* b eps) (* b eps)) 1/2)))
593.0ms
(* (/ (+ (* (pow x 5) 1/60) (+ (* (* (* x x) 1/3) x) (* 2 x))) 2) (sin y))
557.0ms
(/ (* 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))))
504.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
452.0ms
(sqrt (- (* b_2 b_2) (* a c)))
Rules
3490×*-un-lft-identity
3388×add-sqr-sqrt
2702×times-frac
1920×add-cube-cbrt
1285×add-exp-log
1277×pow1
1183×add-cbrt-cube
913×sqrt-prod
608×add-log-exp
513×difference-of-squares
491×associate-*r*
478×associate-*l*
413×distribute-lft-out
390×prod-exp
370×distribute-lft-out--
369×pow-prod-down cbrt-unprod
354×insert-posit16
325×associate-/l*
291×log-prod
233×associate-/r*
196×flip-+ flip3-+
194×div-exp
190×div-inv
189×flip3-- flip--
177×associate-*l/
174×associate-/r/
163×tan-quot
161×swap-sqr
158×cbrt-undiv
153×unswap-sqr
147×frac-times
144×cbrt-prod
143×associate-*r/
136×sqrt-div
132×unpow-prod-down
120×sqrt-pow1 pow-prod-up
100×*-commutative
97×diff-log
96×pow1/2
92×sub-neg
91×log-pow
83×associate-/l/
69×sqr-pow pow-unpow
66×pow-sqr
60×associate-+r+
58×exp-prod
56×frac-2neg clear-num frac-add
52×pow-plus
47×difference-of-sqr-1
42×log-div
39×sum-log
37×distribute-rgt-out
36×exp-sum
34×cbrt-div
33×pow1/3 rem-sqrt-square
31×pow2 distribute-rgt-in distribute-lft-in
27×div-sub
25×frac-sub
24×+-commutative
22×associate-+l+
21×1-exp
19×rem-log-exp
17×distribute-rgt-neg-in associate--l+
15×pow-flip rec-exp
14×exp-diff
12×associate--r+
10×neg-sub0 pow-exp pow-to-exp
9×inv-pow
8×associate--l- pow-pow
7×distribute-rgt-out-- sqrt-unprod
6×associate-+r- associate-+l-
5×sin-sum exp-neg
4×unpow-prod-up neg-log sin-mult sub-div rem-exp-log distribute-rgt1-in
3×sqr-sin pow-div
2×sin-cos-mult log-rec distribute-frac-neg un-div-inv +.c-commutative rem-square-sqrt cos-sum tan-sum associate--r- pow-sub
1×remove-posit16 diff-atan frac-2neg.c cube-unmult sub0-neg pow3 sqrt-pow2 diff-sin diff-cos unsub-neg

localize4.4s (0.7%)

regimes4.3s (0.7%)

Accuracy

Total 39.9b remaining (27.5%)

Threshold costs 5.3b (3.7%)

13.5b36.4%expax (section 3.5)
4.8b83%quadm (p42, negative)
4.6b83.4%quadp (p42, positive)
4.6b83.5%quad2p (problem 3.2.1, positive)
3.0b88.3%quad2m (problem 3.2.1, negative)

bsearch2.1s (0.3%)

end1.0ms (0.0%)