Details

simplify5.2m (42.9%)

sample4.5m (37.2%)

Algorithm
56×intervals
16×halfpoints
Results
49.1s66387×body1280valid
31.0s17053×body2560valid
21.3s42442×body640valid
9.9s12722×body10240exit
9.1s94301×body80valid
7.2s62714×body80nan
5.9s20627×body320valid
2.0s47530×pre80true
1.9s11043×body160valid
617.0ms687×body1280nan
437.0ms504×body5120valid
348.0ms619×body640nan
123.0ms375×body320nan
37.0ms199×body160nan

series56.8s (7.8%)

Calls

407 calls:

2.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* b (+ eps (* (* 1/2 (pow eps 2)) b))) (* 1/6 (* (pow eps 3) (pow b 3))))))
739.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
629.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
612.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
583.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

prune54.1s (7.4%)

rewrite25.0s (3.4%)

Algorithm
121×rewrite-expression-head
Calls

407 calls:

1.1s
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))
563.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
537.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
506.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (+ (* 2.0 (+ (exp x) 2.0)) (exp (+ x x)))) (exp (- x)))
491.0ms
(* (pow eps 2) (+ (* (* 1/6 (pow a 3)) eps) (* 1/2 (pow a 2))))
Rules
5589×times-frac
5576×*-un-lft-identity
5277×add-sqr-sqrt
3345×add-cube-cbrt
2468×sqrt-prod
1382×add-exp-log
1091×add-cbrt-cube
997×cbrt-prod
880×associate-*l*
819×associate-*r*
753×pow1
733×difference-of-squares
697×add-log-exp
670×unpow-prod-down
669×distribute-lft-out
479×distribute-lft-out--
440×associate-/l*
360×prod-exp
322×sqr-pow
316×associate-/r*
285×log-prod
280×div-exp
250×unswap-sqr
239×cube-prod
236×cbrt-unprod
224×swap-sqr
217×div-inv
213×associate-/r/
203×flip-- flip3--
190×cbrt-undiv
155×flip-+ flip3-+
130×log-pow
125×distribute-rgt-neg-in
119×pow-prod-down
117×distribute-lft-neg-in neg-mul-1
109×diff-log
108×sub-neg
106×unpow2
95×sqrt-div
82×associate-*r/
78×*-commutative
76×clear-num frac-2neg
75×associate-/l/
72×sqrt-pow1
66×pow-exp
65×exp-prod
63×pow-to-exp
62×pow1/2
60×pow-unpow
59×cbrt-div
55×associate-*l/
49×sum-log
44×pow1/3
38×log-div
37×rem-sqrt-square
33×distribute-rgt-in distribute-lft-in
31×div-sub
30×+-commutative
29×frac-sub
26×frac-times
25×rem-log-exp
24×frac-add
22×1-exp
21×pow-flip
20×pow-pow rec-exp
18×unpow3 cube-mult
17×tan-quot
16×associate--l+
13×complex-mul-def
12×pow-div
11×difference-cubes associate-+l+ pow-prod-up
10×rem-cube-cbrt neg-sub0 associate--r+
9×exp-diff pow-sqr
8×sin-mult exp-sum associate-+l-
7×inv-pow
6×exp-neg
5×associate--l- sqrt-unprod sin-cos-mult pow-plus sqrt-undiv pow2
4×cube-div *.c-commutative distribute-frac-neg
3×+.c-commutative associate-+r+ cos-mult
2×cos-sum sqr-sin complex-add-def rem-square-sqrt neg-log tan-sum rem-cbrt-cube frac-2neg.c sin-sum
1×sub0-neg un-div-inv rem-exp-log associate-+l+.c associate--r- diff-atan distribute-rgt-out-- diff-cos associate-*l*.c sub-div exp-to-pow diff-sin

regimes4.4s (0.6%)

Accuracy

Total 26.5b remaining (20.2%)

Threshold costs 9.6b (7.3%)

4.5b84.2%quad2p (problem 3.2.1, positive)
4.5b84.2%quadp (p42, positive)
3.1b0%expq3 (problem 3.4.2)
3.1b88.2%quadm (p42, negative)
1.6b82.1%2nthrt (problem 3.4.6)

localize3.5s (0.5%)

bsearch1.8s (0.2%)

end1.0ms (0.0%)