Details

simplify13.6m

Calls

10330 calls:

Slowest
1.5s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x)) (* (* (- x 1) (- x 1)) (- x 1))))
1.4s
(/ (* (* (- 0 (* a c)) (- 0 (* a c))) (- 0 (* a c))) (* (* a a) a))
1.4s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) x) (- x 1)) (* (* (+ x 1) x) (- x 1))) (* (* (+ x 1) x) (- x 1))))
1.4s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.2s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))

sample5.0m

Algorithm
55×intervals
16×halfpoints
Results
1.1m64377×body1280valid
42.7s17315×body2560valid
25.4s40236×body640valid
12.7s11642×body10240exit
10.5s88954×body80valid
8.9s19807×body320valid
6.7s57754×body80nan
2.9s10128×body160valid
1.9s47454×pre80true
824.0ms469×body5120valid
19.0ms19×body1280nan
17.0ms23×body640nan
7.0ms15×body320nan
0.0msbody160nan

prune2.3m

series35.2s

Calls

402 calls:

Slowest
570.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
517.0ms
(+ 1 (+ (log n) (/ -1/6 (* n n))))
508.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
477.0ms
(/ (- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x))) (* (- 1 (* (tan x) (tan eps))) (cos x)))
454.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))

rewrite21.9s

Algorithm
120×rewrite-expression-head
Calls

402 calls:

Slowest
3.7s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
3.2s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
1.2s
(- (+ (/ 1/2 n) (+ 1 (+ (log n) (/ -1/6 (* n n))))) 1)
738.0ms
(cbrt (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))
688.0ms
(cbrt (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))
Rules
3611×*-un-lft-identity
3451×add-sqr-sqrt
3019×times-frac
2659×pow1
2322×add-cube-cbrt
1595×sqrt-prod
1594×add-exp-log
1421×add-cbrt-cube
781×pow-prod-down
680×add-log-exp
584×prod-exp
569×pow-prod-up
539×cbrt-unprod
398×difference-of-squares associate-*l*
393×associate-*r*
390×insert-posit16
362×distribute-lft-out
341×associate-/l*
320×associate-/r*
316×log-prod
286×pow-sqr
263×distribute-lft-out--
242×pow-plus
235×flip3-- flip--
211×flip-+ flip3-+
209×associate-*l/
204×div-exp
191×div-inv
174×associate-/r/
162×pow2
157×swap-sqr
152×sqrt-div
146×sqrt-pow1 cbrt-undiv
139×unswap-sqr
119×frac-times
116×associate-*r/
114×pow1/2
107×sub-neg
103×diff-log
98×pow-unpow
95×*-commutative
85×cbrt-prod
82×associate-/l/
76×unpow-prod-down exp-prod
72×distribute-rgt-neg-in
71×frac-2neg clear-num
69×log-pow
61×pow-flip
60×cbrt-div
53×sum-log difference-of-sqr-1
50×frac-add
49×tan-quot
46×rem-log-exp distribute-lft-neg-in
42×log-div
39×sqr-pow
37×rem-sqrt-square
36×1-exp rec-exp distribute-rgt-in distribute-lft-in
32×+-commutative
27×exp-sum
26×frac-sub pow1/3
24×associate--l+
21×div-sub
17×pow-exp inv-pow
16×pow-to-exp
14×associate--r+
13×complex-mul-def
12×associate--l-
11×pow-pow
10×neg-mul-1 pow-div
associate-+l+ neg-sub0 distribute-lft1-in distribute-rgt-out
sqrt-unprod
neg-log
sin-sum rem-square-sqrt
associate-+r+ sin-mult distribute-rgt-out-- associate-+l- associate--r-
*.c-commutative pow3 distribute-frac-neg +.c-commutative un-div-inv
exp-diff associate-*l*.c cos-mult cube-unmult sub0-neg sqr-sin frac-2neg-c rem-exp-log complex-add-def cos-sum tan-sum rem-cbrt-cube
distribute-lft-neg-out diff-atan sin-cos-mult sub-div exp-to-pow distribute-neg-frac associate-+l+.c diff-sin diff-cos

localize5.0s

regimes4.4s

Accuracy

Total 15.0b remaining (11.6%)

4.7b47.2%expq3 (problem 3.4.2)
3.0b88.3%quadm (p42, negative)
0.9b96.1%quadp (p42, positive)
0.9b96.3%quad2p (problem 3.2.1, positive)
0.9b96.4%quad2m (problem 3.2.1, negative)

bsearch2.6s

end1.0ms