Details

sample4.2m (37.4%)

Algorithm
56×intervals
16×halfpoints
Results
49.4s67068×body1280valid
30.2s17482×body2560valid
17.6s42210×body640valid
8.6s13034×body10240exit
7.9s93334×body80valid
7.7s63525×body80nan
6.3s20810×body320valid
2.2s10561×body160valid
1.5s47297×pre80true
690.0ms655×body1280nan
451.0ms650×body640nan
226.0ms411×body5120valid
136.0ms326×body320nan
37.0ms207×body160nan

simplify4.2m (36.9%)

prune1.6m (13.8%)

series49.5s (7.3%)

Calls

374 calls:

1.4s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.4s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* eps (* (* eps eps) (* (* a a) a)))) (+ (* eps a) (* (* (* eps eps) 1/2) (* a a)))) (- (exp (* b eps)) 1.0)))
716.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
590.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite19.2s (2.8%)

Algorithm
119×rewrite-expression-head
Calls

374 calls:

1.7s
(cbrt (* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps)))))
739.0ms
(+ (* (* (* x a) (* x a)) 1/2) (+ (* x (* (* 1/6 a) (* (* x a) (* x a)))) (* x a)))
578.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* eps (* (* eps eps) (* (* a a) a)))) (+ (* eps a) (* (* (* eps eps) 1/2) (* a a)))) (- (exp (* b eps)) 1.0)))
420.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
382.0ms
(* x (+ (* (* 1/6 a) (* (* x a) (* x a))) a))
Rules
24704×tan-quot
20605×frac-times
9826×associate-*l/
8282×associate-*r/
4128×cbrt-div
4082×*-un-lft-identity
3598×add-sqr-sqrt
3424×times-frac
2226×add-cube-cbrt
1552×sqrt-prod
1249×add-exp-log
1232×pow1
1156×add-cbrt-cube
628×add-log-exp
567×distribute-lft-out
550×difference-of-squares
435×distribute-lft-out--
381×prod-exp
375×pow-prod-down
371×associate-*l*
360×associate-/l*
357×cbrt-unprod
348×associate-/r*
327×associate-*r*
279×log-prod
251×associate-/r/
240×flip3-- flip--
184×div-exp
183×flip-+ flip3-+
181×div-inv
157×sqrt-div
152×cbrt-undiv
151×cbrt-prod
140×unpow-prod-down
121×unswap-sqr
115×swap-sqr sub-neg
106×diff-log
94×log-pow
86×pow-prod-up
83×sqrt-pow1
82×sqr-pow
81×associate-/l/
79×*-commutative
67×frac-2neg clear-num
65×pow1/2
61×exp-prod
60×frac-sub
58×pow-sqr
45×distribute-rgt-neg-in
42×pow1/3
40×distribute-rgt-in distribute-lft-in
39×pow-unpow
36×pow-plus
35×rem-sqrt-square distribute-lft-neg-in
26×sum-log pow2
24×div-sub
23×log-div
22×associate--l+ frac-add
21×rem-log-exp
19×pow3
17×+-commutative
15×difference-cubes
14×1-exp rec-exp complex-mul-def
13×neg-mul-1 associate--r+
7×exp-to-pow
6×associate-+l+ associate--l- pow-exp sub-div pow-to-exp
5×pow-flip associate-+r+ sqrt-unprod exp-lft-cube
4×sin-mult inv-pow rem-exp-log
3×neg-sub0 *.c-commutative neg-log pow-pow +.c-commutative rem-cbrt-cube
2×exp-diff associate-*l*.c cos-mult sin-sum cube-unmult tan-sum distribute-neg-frac distribute-rgt-out-- complex-add-def rem-square-sqrt cos-sum sqr-cos
1×diff-atan associate-+r- frac-2neg.c distribute-neg-out distribute-rgt-neg-out distribute-frac-neg un-div-inv associate-+l- diff-sin associate-+l+.c diff-cos unsub-neg associate--r-

localize5.3s (0.8%)

regimes5.1s (0.7%)

Accuracy

Total 38.3b remaining (26.2%)

Threshold costs 6.3b (4.3%)

13.8b34.6%expax (section 3.5)
4.5b84.1%quadp (p42, positive)
4.5b84.1%quad2p (problem 3.2.1, positive)
4.5b83.3%quadm (p42, negative)
3.5b0%expq3 (problem 3.4.2)

bsearch2.2s (0.3%)

end1.0ms (0.0%)