Details

simplify5.3m (36.7%)

sample5.0m (35.1%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67429×body1280valid
40.6s17389×body2560valid
27.2s41851×body640valid
12.9s12829×body10240exit
12.9s93836×body80valid
9.2s20701×body320valid
7.2s63522×body80nan
2.5s10486×body160valid
2.3s47295×pre80true
749.0ms680×body1280nan
585.0ms685×body640nan
474.0ms489×body5120valid
177.0ms378×body320nan
80.0ms175×body160nan

prune2.7m (19.1%)

series41.8s (4.8%)

Calls

393 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (tan eps))) (cos x)))) (+ 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)))) (tan x))
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 a) (* eps (* (* a eps) (* a eps)))) (+ (* (* 1/2 (* eps a)) (* eps a)) (* eps a))) (- (exp (* b eps)) 1)))
787.0ms
(log (sqrt (exp (* x (+ 1/2 (* x 1/6))))))
686.0ms
(log (sqrt (exp (* (* x x) (* x x)))))

rewrite25.3s (2.9%)

Algorithm
119×rewrite-expression-head
Calls

393 calls:

2.1s
(* (/ 1 (sqrt 2)) (/ (+ (+ (* 1/60 (* (* x x) (* x (* x x)))) (* (* x x) (* 1/3 x))) (* x 2)) (/ (sqrt 2) (sin y))))
1.9s
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ (+ (* 1/60 (* (* x x) (* x (* x x)))) (* (* x x) (* 1/3 x))) (* x 2)) (/ (sqrt 2) (sin y))))
1.5s
(* (cbrt (- (- (* -2/3 (* (* eps eps) eps)) (* 2 eps)) (* 2/5 (pow eps 5)))) (cbrt (- (- (* -2/3 (* (* eps eps) eps)) (* 2 eps)) (* 2/5 (pow eps 5)))))
1.1s
(* (- (exp (* a eps)) 1) (+ (* b (+ (* 1/6 (* eps (* (* eps b) (* eps b)))) eps)) (* (* 1/2 (* eps b)) (* eps b))))
1.0s
(* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27))
Rules
6164×times-frac
5601×add-sqr-sqrt
5289×*-un-lft-identity
3590×add-cube-cbrt
2766×pow1
2047×sqrt-prod
1556×add-exp-log
1317×add-cbrt-cube
864×pow-prod-up
770×cbrt-prod
710×associate-*l*
692×add-log-exp
688×associate-*r*
591×difference-of-squares
584×pow-prod-down
519×pow-plus
485×associate-/l*
455×prod-exp
416×distribute-lft-out--
411×cbrt-unprod
405×distribute-lft-out
382×insert-posit16
370×associate-/r*
350×sqrt-div
327×div-exp
322×pow-sqr
302×div-inv
274×sqrt-pow1
258×unswap-sqr
241×pow-unpow
230×flip3-- flip--
221×cbrt-undiv
208×flip-+ flip3-+
191×pow2
187×unpow-prod-down
184×log-prod
173×log-pow
164×associate-/r/
158×frac-times
156×cbrt-div
152×exp-prod
148×swap-sqr
131×pow1/2
117×associate-*r/
101×associate-*l/
96×diff-log
90×sub-neg
88×*-commutative
86×sqr-pow
75×tan-quot frac-2neg clear-num
72×frac-add
66×sum-log
64×pow3
61×pow1/3
58×associate-/l/
41×pow-flip
40×1-exp rec-exp
39×distribute-rgt-in distribute-lft-in
34×+-commutative
29×associate-+r+ difference-of-sqr-1
28×rem-sqrt-square
27×frac-sub
23×associate--l+
20×inv-pow
19×rem-log-exp
18×log-div
17×associate-+l+ distribute-rgt-neg-in div-sub
16×pow-exp pow-to-exp
13×complex-mul-def
10×pow-div exp-to-pow
9×associate--r+
8×sqrt-unprod associate-+l-
7×neg-sub0 associate--l- pow-pow
6×exp-sum distribute-rgt-out distribute-rgt1-in
5×sin-sum neg-log cos-sum
4×exp-diff sin-mult rem-exp-log
3×associate-+r- *.c-commutative log-rec sum-cubes +.c-commutative sqr-sin rem-square-sqrt
2×associate-*l*.c sin-cos-mult exp-neg tan-sum complex-add-def
1×remove-posit16 diff-atan distribute-rgt-out-- cube-unmult sub0-neg distribute-lft-neg-out frac-2neg-c associate-+l+.c diff-sin diff-cos unsub-neg

localize5.2s (0.6%)

regimes4.9s (0.6%)

Accuracy

Total 23.4b remaining (20.8%)

Threshold costs 5.3b (4.7%)

4.4b84.2%quad2p (problem 3.2.1, positive)
4.4b84.3%quadp (p42, positive)
4.3b-30.1%expq3 (problem 3.4.2)
2.3b90.8%quad2m (problem 3.2.1, negative)
1.4b94.3%quadm (p42, negative)

bsearch1.8s (0.2%)

end1.0ms (0.0%)