Details

sample5.0m (52.0%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66759×body1280valid
38.8s17648×body2560valid
27.6s41715×body640valid
15.2s12438×body10240exit
11.2s94099×body80valid
8.9s20948×body320valid
7.5s63993×body80nan
3.1s10800×body160valid
2.0s47361×pre80true
801.0ms670×body1280nan
731.0ms706×body640nan
414.0ms434×body5120valid
241.0ms366×body320nan
61.0ms220×body160nan

simplify2.6m (26.9%)

prune58.7s (10.1%)

series37.9s (6.5%)

Calls

399 calls:

987.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
958.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
669.0ms
(/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
668.0ms
(/ (/ (+ 0 (* a c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
577.0ms
(/ (/ (+ 1 0) (+ (sqrt x) (sqrt (+ x 1)))) (sqrt (+ x 1)))

rewrite14.9s (2.6%)

Algorithm
121×rewrite-expression-head
Calls

399 calls:

1.3s
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (cbrt (* (* (* (sin x) (sin eps)) (* (sin x) (tan eps))) (* (tan x) (sin eps)))) (cbrt (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))))) (tan x))
411.0ms
(+ (* (* 1/6 x) (* (* (* a x) (* a x)) a)) (+ (* 1/2 (* (* a x) (* a x))) (* a x)))
409.0ms
(* x (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 1/3)))
254.0ms
(* (* 1/6 x) (* (* (* a x) (* a x)) a))
229.0ms
(* (/ (+ (+ (+ x x) (* x (* (* x x) 1/3))) (* 1/60 (pow x 5))) 2) (sin y))
Rules
5650×*-un-lft-identity
4450×times-frac
4252×add-sqr-sqrt
2770×add-cube-cbrt
2055×sqrt-prod
1378×add-exp-log
1344×pow1
1250×add-cbrt-cube
1177×distribute-lft-out
756×associate-*r*
686×add-log-exp
603×associate-*l*
530×difference-of-squares
462×associate-/l*
416×prod-exp
392×insert-posit16
385×distribute-lft-out--
374×cbrt-unprod
364×pow-prod-down
303×associate-/r*
296×cbrt-prod
275×cbrt-div flip-+ flip3-+
271×frac-times
267×div-inv
254×tan-quot
245×log-prod
236×div-exp
234×associate-*l/
183×cbrt-undiv
181×associate-/r/
177×unswap-sqr
176×flip3-- flip--
169×associate-*r/
155×unpow-prod-down
147×log-pow
118×sqrt-div
108×exp-prod
102×pow-prod-up
96×distribute-rgt-neg-in
92×sub-neg diff-log
90×swap-sqr
89×*-commutative
88×distribute-lft-neg-in
87×sqr-pow
70×pow-sqr
66×frac-2neg clear-num pow1/3
63×sum-log associate-/l/
59×pow-plus
49×sqrt-pow1 pow1/2 frac-add
42×log-div
39×pow-unpow
37×associate-+r+
36×associate-+l+ pow2
34×+-commutative
33×rem-sqrt-square
32×distribute-rgt-in distribute-lft-in
31×pow-flip
28×1-exp rec-exp
25×div-sub
21×difference-of-sqr-1
20×associate--l+
19×rem-log-exp
16×exp-sum
15×associate--r+
14×inv-pow
11×frac-sub
10×cos-mult difference-of-sqr--1
9×pow-exp pow-to-exp
8×associate--l- distribute-neg-frac
7×sin-mult rem-exp-log
6×neg-sub0 pow-div pow3
5×exp-diff neg-log associate-+l- distribute-rgt1-in
4×distribute-lft-neg-out neg-mul-1 rem-cbrt-cube distribute-rgt-out
3×associate-+r- exp-to-pow pow-pow distribute-rgt-out-- sqr-sin
2×sin-sum cube-unmult distribute-lft1-in sqrt-unprod tan-sum exp-neg +.c-commutative cos-sum associate--r- count-2
1×remove-posit16 diff-atan frac-2neg.c sin-cos-mult sub-div un-div-inv diff-sin distribute-neg-in diff-cos

regimes5.1s (0.9%)

Accuracy

Total 28.1b remaining (21.7%)

Threshold costs 4.9b (3.8%)

4.9b82.4%quadp (p42, positive)
4.9b82.2%quad2p (problem 3.2.1, positive)
4.7b82.4%quad2m (problem 3.2.1, negative)
4.6b82.7%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)

localize4.5s (0.8%)

bsearch1.5s (0.3%)

end1.0ms (0.0%)