Details

sample5.8m (42.9%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67065×body1280valid
39.9s17266×body2560valid
24.4s42459×body640valid
13.4s13136×body10240exit
11.0s93630×body80valid
8.0s20634×body320valid
5.4s63853×body80nan
3.3s47482×pre80true
2.6s10812×body160valid
870.0ms670×body1280nan
508.0ms702×body640nan
425.0ms461×body5120valid
211.0ms377×body320nan
48.0ms198×body160nan

simplify4.4m (32.3%)

prune1.5m (11.0%)

series59.1s (7.3%)

Calls

381 calls:

2.9s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
1.0s
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
709.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
655.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))
635.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (log (exp (* (sin eps) (tan x)))) (cos eps)))) (tan x))

rewrite37.3s (4.6%)

Algorithm
120×rewrite-expression-head
Calls

381 calls:

3.4s
(+ (+ (* 1/2 (/ (pow eps 2) (pow 1.0 2))) (log (sqrt 1.0))) (+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3)))))
1.8s
(* (/ (cbrt 1.0) (cbrt (/ (+ x 1.0) (- 1.0)))) (/ (cbrt 1.0) (cbrt (/ (+ x 1.0) (- 1.0)))))
1.3s
(+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3))))
1.3s
(+ (/ (- (pow (/ 1.0 N) 3) (pow (/ 0.5 (* N N)) 3)) (+ (* (/ 1.0 N) (/ 1.0 N)) (* (/ 0.5 (* N N)) (+ (/ 0.5 (* N N)) (/ 1.0 N))))) (/ 0.3333333333333333 (pow N 3)))
961.0ms
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
Rules
9199×times-frac
8272×*-un-lft-identity
7667×add-sqr-sqrt
4732×add-cube-cbrt
2730×cbrt-prod
2575×sqrt-prod
1230×add-exp-log
1095×associate-*l*
1090×distribute-lft-out
1086×associate-*r*
1066×unpow-prod-down
1026×difference-of-squares
940×add-cbrt-cube
722×add-log-exp
672×distribute-rgt-neg-in
646×pow1
596×cube-prod
587×distribute-lft-out--
581×associate-/l* swap-sqr
540×distribute-lft-neg-in
426×associate-/r*
406×sqr-pow
366×log-prod
345×unswap-sqr
280×prod-exp div-exp
254×div-inv
218×flip-- flip3--
211×associate-/r/
190×cbrt-undiv
180×neg-mul-1
158×sqrt-div
157×cbrt-unprod
156×exp-sum
146×flip-+ flip3-+
144×unpow2
109×diff-log
104×sub-neg
99×log-pow
82×associate-/l/ sqrt-pow1
80×frac-2neg sum-log clear-num
78×pow-exp
77×associate-*r/
75×pow-to-exp
73×pow-unpow
71×associate-*l/
70×pow-prod-down
68×frac-times
67×frac-add
64×pow1/2
63×*-commutative
60×exp-prod
46×cbrt-div
44×associate-+r+ log-div
35×frac-sub
31×+-commutative
30×pow1/3
28×div-sub
27×rem-sqrt-square
24×distribute-rgt-in distribute-lft-in
23×unpow3 cube-mult
22×pow-prod-up 1-exp tan-quot
21×rec-exp
19×exp-diff associate-+l+
18×rem-log-exp pow-pow
16×associate--r+
15×neg-sub0
14×difference-cubes pow-sqr
13×complex-mul-def associate--l+
12×neg-log
11×cube-div rem-exp-log associate--l-
10×associate-+l-
9×pow-flip
8×rem-cube-cbrt exp-to-pow
7×distribute-neg-in
6×exp-lft-sqr
5×sqrt-undiv inv-pow pow2 pow-plus
4×sqrt-unprod un-div-inv distribute-rgt-out-- sin-mult *.c-commutative
3×sqrt-pow2 +.c-commutative rem-square-sqrt
2×cos-sum sin-sum exp-neg sub-div complex-add-def tan-sum rem-cbrt-cube
1×sin-cos-mult associate-+r- associate-+l+.c associate--r- diff-atan diff-cos associate-*l*.c diff-sin

regimes7.3s (0.9%)

Accuracy

Total 28.2b remaining (18.8%)

Threshold costs 6.2b (4.1%)

5.1b82.7%quadp (p42, positive)
4.6b83.2%quad2p (problem 3.2.1, positive)
4.5b84.2%quadm (p42, negative)
3.3b0%expq3 (problem 3.4.2)
2.1b75.9%2nthrt (problem 3.4.6)

localize5.6s (0.7%)

bsearch2.8s (0.3%)

end1.0ms (0.0%)