Details

sample1.8m (53.3%)

Algorithm
56×intervals
16×halfpoints
Results
24.8s67058×body1280valid
16.6s17165×body2560valid
8.5s42691×body640valid
3.9s12625×body10240exit
2.9s93767×body80valid
2.6s20629×body320valid
1.6s63163×body80nan
871.0ms10728×body160valid
548.0ms47304×pre80true
317.0ms698×body1280nan
214.0ms658×body640nan
139.0ms474×body5120valid
72.0ms383×body320nan
20.0ms187×body160nan

prune38.4s (18.7%)

series31.9s (15.5%)

Calls

389 calls:

930.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
893.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
507.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
503.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
470.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify11.0s (5.4%)

Algorithm
195×egg-herbie

rewrite8.3s (4.1%)

Algorithm
123×rewrite-expression-head
Calls

389 calls:

570.0ms
(- 1.0 (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
324.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
196.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
188.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
182.0ms
(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
Rules
17527×times-frac
11710×add-sqr-sqrt
11535×*-un-lft-identity
7993×add-cube-cbrt
2562×sqrt-prod
1668×add-exp-log
1565×difference-of-squares
1304×distribute-lft-out--
1093×add-cbrt-cube
1033×associate-/l*
991×associate-*r*
943×unpow-prod-down
776×pow1
756×add-log-exp
736×associate-*l*
581×div-inv
566×associate-/r*
544×div-exp
510×distribute-lft-out
419×sqr-pow
358×prod-exp
319×cube-prod
317×associate-/r/ distribute-rgt-neg-in
299×unswap-sqr
292×flip-- flip3--
251×cbrt-undiv
207×cbrt-prod
195×unpow2
189×cbrt-unprod
188×log-prod
148×flip-+ flip3-+
134×sqrt-pow1
129×diff-log
127×sub-neg
119×log-pow associate-*l/
115×pow-prod-down
114×pow-exp
108×pow-to-exp
105×associate-*r/
97×pow-unpow
90×pow1/2
89×associate-/l/
83×1-exp frac-times
80×clear-num frac-2neg
77×sum-log
75×exp-prod
71×*-commutative
68×rec-exp
64×tan-quot
63×sqrt-div
60×swap-sqr
58×frac-add
57×distribute-rgt-in distribute-lft-in
50×pow-prod-up
46×unpow3 cube-mult
41×frac-sub
40×+-commutative
38×associate-+r+
35×cbrt-div
32×rem-sqrt-square
28×log-div
27×pow-pow associate--l+
25×pow-flip div-sub
24×complex-mul-def
23×pow1/3
22×associate-+l+ pow-sqr
21×associate--r+
18×neg-sub0 rem-log-exp
17×associate--l-
16×exp-sum
15×neg-log
14×rem-cube-cbrt
13×cos-mult
11×inv-pow
10×pow-div associate-+l-
8×difference-cubes sqrt-unprod
7×cube-div pow-plus
6×exp-diff *.c-commutative
5×pow2 exp-to-pow
4×rem-exp-log associate--r- difference-of-sqr-1 +.c-commutative complex-add-def sin-mult
3×un-div-inv associate-+r- rem-square-sqrt sqrt-undiv
2×cos-sum associate-+l+.c exp-neg associate-*l*.c tan-sum distribute-rgt-neg-out frac-2neg.c rem-cbrt-cube sin-sum log-rec
1×sqrt-pow2 sum-cubes diff-atan sin-cos-mult diff-cos unsub-neg sub-div diff-sin

regimes2.9s (1.4%)

Accuracy

Total 25.6b remaining (11.7%)

Threshold costs 5.9b (2.7%)

4.8b82%quadp (p42, positive)
3.6b87.3%quadm (p42, negative)
3.5b0%expq3 (problem 3.4.2)
3.0b88.8%quad2p (problem 3.2.1, positive)
1.7b82.1%2cos (problem 3.3.5)

localize1.9s (0.9%)

bsearch1.5s (0.7%)

end1.0ms (0.0%)