Details

simplify6.4m (52.5%)

sample3.6m (29.5%)

Algorithm
50×intervals
15×halfpoints
Results
42.9s56632×body1280valid
25.6s12488×body2560valid
18.7s37824×body640valid
6.1s67701×body80valid
4.9s18747×body320valid
3.0s44715×body80nan
2.8s9074×body160valid
1.3s1602×body10240exit
770.0ms37462×pre80true
609.0ms667×body1280nan
350.0ms649×body640nan
174.0ms243×body5120valid
110.0ms338×body320nan
35.0ms187×body160nan

prune51.8s (7.1%)

series45.2s (6.2%)

Calls

370 calls:

2.0s
(log (exp (* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
1.4s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
757.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
746.0ms
(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
580.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite23.6s (3.2%)

Algorithm
116×rewrite-expression-head
Calls

370 calls:

2.6s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
2.3s
(/ (log (- 1.0 x)) (- (- (log 1.0) (+ (* (* (/ (* x x) 1.0) (/ (* x x) 1.0)) 1/2) (* 1.0 (* x x)))) (log (- 1.0 x))))
1.4s
(* x (+ (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333) (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)))))
1.0s
(/ (+ (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)) (- (* 0.3333333333333333 0.3333333333333333) (* (* (* x x) 0.022222222222222223) 0.3333333333333333))) (+ (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333) (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)))))
932.0ms
(/ x (/ (+ (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223)) (- (* 0.3333333333333333 0.3333333333333333) (* (* (* x x) 0.022222222222222223) 0.3333333333333333))) (+ (* (* 0.3333333333333333 0.3333333333333333) 0.3333333333333333) (* (* (* x x) 0.022222222222222223) (* (* (* x x) 0.022222222222222223) (* (* x x) 0.022222222222222223))))))
Rules
4717×*-un-lft-identity
4415×times-frac
4316×add-sqr-sqrt
2763×add-cube-cbrt
2608×sqrt-prod
1702×pow1
1338×add-exp-log
1242×add-cbrt-cube
728×associate-*l*
655×add-log-exp
609×difference-of-squares
521×distribute-lft-out
511×distribute-lft-out--
504×pow-prod-down
432×prod-exp
413×associate-/l*
403×cbrt-unprod
342×log-prod
337×associate-*r*
271×associate-/r*
220×flip3-- flip--
200×div-exp
199×pow-prod-up log-pow
195×div-inv
170×cbrt-undiv
155×associate-/r/
140×exp-prod
139×flip-+ flip3-+
135×swap-sqr pow-sqr
131×cbrt-prod
129×sub-neg
123×associate-*r/
122×unpow-prod-down
120×unswap-sqr
109×diff-log
101×sqrt-pow1 pow-plus
86×*-commutative
83×associate-*l/
81×distribute-rgt-neg-in
79×sqrt-div
75×frac-times
73×distribute-lft-neg-in
69×distribute-rgt-in distribute-lft-in
68×sqr-pow
66×frac-2neg clear-num
65×pow2
61×associate-/l/
59×cbrt-div
58×pow1/2
55×log-div
53×associate--l+
52×pow-unpow
49×sum-log
46×frac-sub
37×pow1/3 rem-log-exp
32×associate--r+
31×pow3
30×cube-unmult div-sub
28×exp-sum +-commutative
27×sum-cubes rem-sqrt-square
26×tan-quot
24×neg-mul-1
21×frac-add
17×pow-flip
15×exp-diff
14×complex-mul-def
13×cos-mult
11×associate-+l+ sqr-cos
10×associate--l- 1-exp pow-div rec-exp
neg-sub0 associate-+r+ sin-mult
pow-exp pow-to-exp
sin-sum sqrt-unprod sub-div
distribute-frac-neg pow-pow distribute-neg-frac rem-exp-log associate-+l- distribute-rgt-out--
*.c-commutative inv-pow un-div-inv +.c-commutative cos-sum associate--r-
associate-*l*.c associate-+r- exp-neg neg-log exp-to-pow complex-add-def rem-square-sqrt tan-sum distribute-neg-in distribute-rgt-out
diff-atan frac-2neg.c sin-cos-mult distribute-rgt-neg-out difference-cubes diff-sin associate-+l+.c rem-cbrt-cube diff-cos

localize5.1s (0.7%)

regimes4.6s (0.6%)

Accuracy

Total 15.5b remaining (14.4%)

Threshold costs 5.5b (5.1%)

5.7b80.2%quad2p (problem 3.2.1, positive)
2.7b89.7%quad2m (problem 3.2.1, negative)
1.6b80.5%2nthrt (problem 3.4.6)
0.9b87.3%2tan (problem 3.3.2)
0.7b0%qlog (example 3.10)

bsearch1.3s (0.2%)

end1.0ms (0.0%)