Details

sample4.5m (40.3%)

Algorithm
56×intervals
16×halfpoints
Results
50.4s67124×body1280valid
33.3s17607×body2560valid
17.5s41562×body640valid
10.0s12697×body10240exit
9.3s94260×body80valid
7.7s20617×body320valid
5.2s63809×body80nan
2.9s10627×body160valid
2.0s47496×pre80true
492.0ms668×body1280nan
436.0ms510×body5120valid
418.0ms675×body640nan
198.0ms365×body320nan
77.0ms188×body160nan

simplify4.0m (36.2%)

series1.1m (9.6%)

Calls

397 calls:

1.8s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.8s
(cbrt (* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
1.6s
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
1.6s
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
1.5s
(cbrt (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

prune59.7s (8.9%)

rewrite22.4s (3.4%)

Algorithm
122×rewrite-expression-head
Calls

397 calls:

1.1s
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
898.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
559.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0)) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) 1.0)))
553.0ms
(* (/ 1 (sqrt 2.0)) (* (* (/ 1 (sqrt (sqrt 2.0))) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt (sqrt 2.0)))) (sin y)))
464.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
11694×times-frac
10071×*-un-lft-identity
8731×add-sqr-sqrt
5626×add-cube-cbrt
3483×sqrt-prod
1663×add-exp-log
1301×distribute-lft-out
1276×difference-of-squares
1225×unpow-prod-down
1060×add-cbrt-cube
1028×distribute-lft-out--
1000×cbrt-prod
934×associate-/l*
764×associate-*r*
742×add-log-exp
714×pow1
662×cube-prod
541×frac-sub
490×associate-*l*
463×div-exp
448×prod-exp
446×sqr-pow
444×associate-/r*
437×log-prod
399×flip-- flip3-- frac-times
393×associate-*l/
379×associate-/r/
331×unswap-sqr
330×div-inv
270×associate-*r/
236×cbrt-undiv
192×cbrt-unprod
187×distribute-rgt-neg-in
177×unpow2
175×pow-unpow
170×flip-+ flip3-+
166×associate-/l/
134×diff-log
131×pow-to-exp pow-exp
130×sub-neg
120×sqrt-div
102×log-pow
96×pow-prod-down
92×cbrt-div
85×swap-sqr
77×frac-2neg clear-num
76×exp-prod
70×*-commutative
65×sqrt-pow1
64×tan-quot
62×1-exp
53×pow1/2 rem-sqrt-square rec-exp
52×frac-add
50×sum-log
49×unpow3 cube-mult
45×pow1/3
37×associate--l+
36×distribute-rgt-in distribute-lft-in
35×log-div
31×associate-+r+
29×rem-log-exp
28×pow-pow div-sub
26×cube-div
25×+-commutative
24×complex-mul-def
20×pow-prod-up associate-+l+
19×associate--l- neg-sub0
17×pow-sqr
16×associate--r+
15×neg-log pow-flip
13×associate-+l-
12×rem-exp-log
11×exp-to-pow
pow-plus
sub-div pow2 exp-sum
inv-pow
exp-diff associate-+r- cos-mult *.c-commutative
difference-cubes sqrt-unprod sin-mult
+.c-commutative complex-add-def
rem-cube-cbrt sin-cos-mult associate-+l+.c exp-neg distribute-rgt-out-- difference-of-sqr-1 unsub-neg associate-*l*.c cos-sum tan-sum sin-sum
sqrt-pow2 un-div-inv diff-atan diff-cos rem-square-sqrt rem-cbrt-cube frac-2neg.c diff-sin

regimes4.5s (0.7%)

Accuracy

Total 46.1b remaining (16.4%)

Threshold costs 7.1b (2.5%)

21.9b-4313.3%2sin (example 3.3)
4.2b52.8%expq3 (problem 3.4.2)
3.3b88.5%quadm (p42, negative)
2.9b89.3%quad2p (problem 3.2.1, positive)
1.6b93.6%quad2m (problem 3.2.1, negative)

localize3.9s (0.6%)

bsearch2.6s (0.4%)

end2.0ms (0.0%)