Details

simplify9.6m (53.5%)

sample5.0m (28.1%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66984×body1280valid
41.1s17605×body2560valid
25.6s41893×body640valid
14.6s12712×body10240exit
11.4s93924×body80valid
8.5s20786×body320valid
6.6s64007×body80nan
3.3s10563×body160valid
2.0s47357×pre80true
882.0ms463×body5120valid
796.0ms680×body1280nan
562.0ms696×body640nan
177.0ms359×body320nan
51.0ms192×body160nan

prune2.3m (12.6%)

series34.4s (3.2%)

Calls

382 calls:

552.0ms
(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2))))) (* a x))
504.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
495.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))
426.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (pow x (/ (/ 1 n) 2)))
373.0ms
(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))

rewrite17.3s (1.6%)

Algorithm
121×rewrite-expression-head
Calls

382 calls:

1.7s
(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (sqrt (exp (* a x)))))) (* a x))
1.7s
(+ (+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2))))) (* a x))
1.7s
(- (+ (+ (+ (/ 1/2 n) (log n)) (/ -1/6 (* n n))) 1) 1)
422.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
323.0ms
(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (* (* a x) (log (exp (* (* a x) 1/2)))))
Rules
4778×*-un-lft-identity
4183×times-frac
4140×add-sqr-sqrt
2725×add-cube-cbrt
2512×sqrt-prod
2216×pow1
1434×add-exp-log
1163×add-cbrt-cube
766×distribute-lft-out
676×add-log-exp
534×pow-prod-down
527×pow-prod-up
444×prod-exp
435×difference-of-squares
430×associate-*r*
424×associate-/l*
417×associate-*l*
375×insert-posit16
371×log-prod
348×cbrt-unprod
330×flip-+ flip3-+
272×distribute-lft-out--
271×associate-/r*
268×div-inv
262×cbrt-prod pow-sqr
254×div-exp
230×associate-*l/
220×frac-times
213×flip3-- flip--
209×sqrt-pow1
202×pow-plus
201×associate-/r/
200×sqrt-div
197×unswap-sqr
180×swap-sqr
157×cbrt-undiv
146×cbrt-div
142×pow2
140×associate-*r/
130×unpow-prod-down
124×frac-add
123×pow-flip
111×pow1/2
95×diff-log
94×sub-neg
87×*-commutative
81×pow-unpow
78×associate-/l/
69×tan-quot exp-prod
68×sqr-pow
66×frac-2neg clear-num
63×log-pow
60×difference-of-sqr--1
54×distribute-rgt-in distribute-lft-in
53×1-exp rec-exp
51×sum-log
42×pow1/3
40×rem-sqrt-square log-div
38×frac-sub
34×inv-pow rem-log-exp
32×+-commutative
31×exp-diff
24×associate--l+
23×exp-to-pow
21×associate-+r+
20×exp-lft-cube
18×div-sub
17×exp-sum
16×associate-+l+ pow-div
15×associate--r+
14×distribute-rgt-neg-in
13×difference-of-sqr-1
10×pow-exp pow3 un-div-inv pow-to-exp
9×associate--l- pow-pow
8×distribute-rgt-out-- distribute-rgt-out distribute-rgt1-in
7×neg-sub0
6×sqrt-unprod rem-exp-log
5×sin-sum neg-log sub-div
4×sin-mult rem-square-sqrt
3×sum-cubes sqr-sin associate-+l- rem-cbrt-cube
2×sin-cos-mult tan-sum exp-neg +.c-commutative cos-sum
1×diff-atan cos-mult frac-2neg.c cube-unmult log-rec sqrt-pow2 diff-sin diff-cos

localize5.2s (0.5%)

regimes4.7s (0.4%)

Accuracy

Total 27.3b remaining (23.7%)

Threshold costs 5.2b (4.5%)

5.7b79.7%quadm (p42, negative)
4.4b84.7%quadp (p42, positive)
4.3b84.5%quad2p (problem 3.2.1, positive)
3.2b87.7%quad2m (problem 3.2.1, negative)
3.0b0%expq3 (problem 3.4.2)

bsearch1.3s (0.1%)

end1.0ms (0.0%)