Details

simplify4.5m (38.5%)

sample4.3m (37.3%)

Algorithm
56×intervals
16×halfpoints
Results
50.7s67068×body1280valid
32.6s17482×body2560valid
20.3s42210×body640valid
10.1s13034×body10240exit
9.1s93334×body80valid
5.9s20810×body320valid
5.0s63525×body80nan
3.0s10561×body160valid
1.8s47297×pre80true
639.0ms655×body1280nan
363.0ms650×body640nan
257.0ms411×body5120valid
115.0ms326×body320nan
43.0ms207×body160nan

prune1.6m (13.6%)

series47.3s (6.8%)

Calls

370 calls:

1.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
666.0ms
(/ (+ 0 (* a c)) (* a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
592.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))
573.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
536.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite13.9s (2.0%)

Algorithm
117×rewrite-expression-head
Calls

370 calls:

414.0ms
(- x (sin x))
404.0ms
(+ (+ (/ (/ 2.0 x) (* x x)) (/ 2.0 (pow x 7))) (/ 2.0 (pow x 5)))
377.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
372.0ms
(- (/ (- (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (* (sin x) (sin eps)) (* (sin x) (sin eps)))) (+ (* (cos x) (cos eps)) (* (sin x) (sin eps)))) (cos x))
279.0ms
(* x (* (* 1/6 a) (* (* x a) (* x a))))
Rules
10164×*-un-lft-identity
8781×times-frac
7755×add-sqr-sqrt
6452×add-cube-cbrt
3651×sqrt-prod
3508×prod-diff
1579×distribute-lft-out
1311×add-exp-log
1169×add-cbrt-cube
979×pow1
857×unpow-prod-down
611×add-log-exp
557×div-inv
523×associate-/l*
513×difference-of-squares
509×associate-*l*
480×fma-neg
408×associate-/r*
397×distribute-lft-out--
391×associate-/r/
360×expm1-log1p-u
359×log1p-expm1-u
345×prod-exp
309×cbrt-unprod
291×associate-*r*
287×sqr-pow
282×div-exp
259×log-prod
244×pow-prod-down
238×associate-+l+
232×swap-sqr
226×fma-def
224×cbrt-undiv
218×flip3-- flip--
196×flip-+ flip3-+
183×cbrt-prod
181×log-pow
171×distribute-rgt-neg-in
169×sqrt-div
154×exp-prod distribute-lft-neg-in
145×distribute-rgt-in distribute-lft-in
138×associate-*l/
110×unswap-sqr
106×sub-neg
102×diff-log
94×associate-/l/
88×frac-times
83×frac-2neg clear-num
80×associate-*r/
70×cbrt-div
69×sqrt-pow1
61×pow-prod-up
56×*-commutative
55×pow1/2
51×neg-mul-1
44×pow1/3
39×frac-sub pow-unpow rem-sqrt-square
35×pow-sqr
32×div-sub fma-udef
31×cos-mult
30×sin-mult
27×tan-quot
26×sum-log
25×pow-plus
24×associate--l+ frac-add log-div
22×1-exp rec-exp rem-log-exp
19×pow2
16×+-commutative
15×exp-sum
14×complex-mul-def
11×neg-sub0 pow-flip
10×associate--l-
8×distribute-neg-frac hypot-def
7×pow-exp neg-log sub-div inv-pow pow-to-exp
6×associate--r+
5×associate-+r- associate-+r+ rem-exp-log
4×quot-tan exp-diff cube-unmult pow-div distribute-frac-neg unsub-neg
3×sin-cos-mult *.c-commutative pow3 pow-pow +.c-commutative
2×associate-*l*.c sin-sum sqrt-unprod exp-to-pow distribute-rgt-out-- complex-add-def rem-square-sqrt cos-sum sqr-cos tan-sum distribute-neg-in
1×expm1-log1p expm1-udef diff-atan frac-2neg.c distribute-rgt-neg-out log1p-expm1 un-div-inv associate-+l- diff-sin associate-+l+.c difference-cubes log1p-udef diff-cos distribute-rgt-out

regimes6.1s (0.9%)

Accuracy

Total 29.1b remaining (19.5%)

Threshold costs 4.7b (3.1%)

4.5b84.2%quad2p (problem 3.2.1, positive)
4.5b84.1%quadp (p42, positive)
4.5b83.2%quad2m (problem 3.2.1, negative)
4.3b84.8%quadm (p42, negative)
3.5b0%expq3 (problem 3.4.2)

localize5.5s (0.8%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)