Details

simplify8.8m (50.9%)

sample5.1m (29.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66920×body1280valid
41.1s17373×body2560valid
26.1s42430×body640valid
14.5s12861×body10240exit
12.9s94107×body80valid
9.7s20470×body320valid
6.8s62875×body80nan
2.8s10312×body160valid
1.8s47506×pre80true
1.2s655×body1280nan
950.0ms450×body5120valid
503.0ms633×body640nan
202.0ms344×body320nan
54.0ms198×body160nan

prune2.4m (13.9%)

series34.4s (3.3%)

Calls

371 calls:

1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
476.0ms
(log (+ (cbrt (* (* (* x (* x x)) (* x (* x x))) (* x (* x x)))) 1))
472.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
472.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite14.0s (1.3%)

Algorithm
118×rewrite-expression-head
Calls

371 calls:

824.0ms
(/ (+ (* 4 (* (* x x) x)) (+ (* (* (* x x) (* x x)) 13/4) (* 3 (* x x)))) (* (+ (exp x) 2) (exp x)))
406.0ms
(/ (- 1 (cos x)) (* x x))
312.0ms
(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (* (* a x) 1/2)))
311.0ms
(* (* (* a x) (* (* a x) (* a x))) 1/6)
309.0ms
(cbrt (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))))
Rules
5505×times-frac
5468×*-un-lft-identity
4634×add-sqr-sqrt
3365×add-cube-cbrt
3274×sqrt-prod
1769×add-exp-log
1724×pow1
1407×add-cbrt-cube
818×distribute-lft-out
667×associate-*r*
648×add-log-exp
645×associate-*l*
577×prod-exp
501×associate-/l*
499×pow-prod-down
491×difference-of-squares
478×cbrt-unprod
396×associate-/r*
386×div-exp
363×insert-posit16
324×cbrt-prod
282×distribute-lft-out--
258×pow-prod-up
256×div-inv
241×cbrt-undiv
227×associate-/r/
222×log-prod
179×unpow-prod-down
178×flip-+ flip3-+
170×pow-sqr
156×flip3-- flip--
144×unswap-sqr
126×pow-plus
114×pow-unpow
109×associate-*l/
105×tan-quot
101×sqrt-pow1
92×frac-times
91×sqr-pow
88×pow2
86×*-commutative associate-*r/
82×diff-log
81×frac-2neg clear-num exp-prod
80×sqrt-div swap-sqr
79×sub-neg
74×associate-/l/
67×pow1/2
66×cbrt-div
57×1-exp rec-exp
55×log-pow
47×pow-flip
46×sum-log
43×pow1/3
39×exp-to-pow
29×+-commutative
28×rem-log-exp
26×distribute-rgt-in distribute-lft-in log-div
25×associate--l+
23×cube-prod
22×rem-sqrt-square
21×frac-sub inv-pow
20×pow-exp difference-of-sqr-1 exp-lft-cube
19×pow-to-exp
18×pow-pow div-sub frac-add
16×pow-div
13×distribute-rgt-neg-in
12×distribute-rgt-out distribute-rgt1-in
11×associate--r+
7×associate-+r+ associate--l-
6×neg-sub0
5×associate-+l+ sqrt-unprod difference-of-sqr--1
4×cube-unmult neg-log sin-mult difference-cubes distribute-neg-frac rem-exp-log
3×pow3 sum-cubes sqr-sin un-div-inv rem-square-sqrt
2×exp-diff sin-sum sqrt-undiv tan-sum frac-2neg-c exp-neg +.c-commutative associate-+l- cos-sum rem-cbrt-cube
1×diff-atan rem-cube-cbrt sin-cos-mult exp-sum distribute-rgt-neg-out sub0-neg unpow3 log-rec sub-div sqrt-pow2 associate-+r- diff-sin cube-mult diff-cos associate--r-

localize4.7s (0.5%)

regimes4.6s (0.4%)

Accuracy

Total 21.7b remaining (17.3%)

Threshold costs 5.1b (4.1%)

4.4b84.1%quadp (p42, positive)
4.4b84.2%quad2p (problem 3.2.1, positive)
3.4b0%expq3 (problem 3.4.2)
1.7b93.2%quad2m (problem 3.2.1, negative)
1.4b91.1%2nthrt (problem 3.4.6)

bsearch2.8s (0.3%)

end1.0ms (0.0%)