Details

simplify4.9m (41.2%)

sample4.3m (36.4%)

Algorithm
56×intervals
16×halfpoints
Results
50.7s67113×body1280valid
33.4s17237×body2560valid
19.8s42016×body640valid
10.6s12757×body10240exit
8.5s93998×body80valid
5.5s20566×body320valid
4.6s62518×body80nan
1.9s47509×pre80true
1.8s10871×body160valid
640.0ms647×body1280nan
484.0ms708×body640nan
350.0ms438×body5120valid
118.0ms362×body320nan
35.0ms187×body160nan

prune1.7m (14.0%)

series38.7s (5.4%)

Calls

356 calls:

538.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
533.0ms
(/ (* (expm1 (* (+ a b) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
524.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
513.0ms
(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
505.0ms
(fma 1 (pow (+ 1 x) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite9.9s (1.4%)

Algorithm
114×rewrite-expression-head
Calls

356 calls:

539.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
247.0ms
(* (* (* eps eps) (* eps (* eps eps))) -2/5)
198.0ms
(* (* (* eps eps) (* eps (* eps eps))) -2/5)
147.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))
146.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
Rules
14351×times-frac
13789×*-un-lft-identity
12478×add-sqr-sqrt
9136×add-cube-cbrt
7284×prod-diff
2668×pow1
2382×sqrt-prod
1624×difference-of-squares
1387×add-exp-log
1240×add-cbrt-cube
1147×distribute-lft-out--
1069×div-inv
963×distribute-lft-out
828×pow-prod-up
686×associate-/r/
624×fma-neg
561×add-log-exp
536×pow-prod-down
423×prod-exp
384×cbrt-unprod
372×associate-*l*
365×associate--r+
359×associate-/l*
358×pow-sqr
356×flip3-- flip--
352×log1p-expm1-u
350×expm1-log1p-u
349×insert-posit16
337×pow-plus
299×distribute-rgt-neg-in
298×associate-*r*
276×associate-+l+
273×div-exp
270×distribute-lft-neg-in
268×associate-/r*
260×sqrt-div
259×cbrt-prod
234×pow2
223×cbrt-undiv
211×flip-+ flip3-+
195×log-prod
144×associate-*l/
132×unpow-prod-down
128×pow-unpow
115×unswap-sqr
94×fma-def
93×difference-of-sqr-1
90×neg-mul-1
89×swap-sqr
86×log-pow diff-log
82×sub-neg
75×sqrt-pow1
73×pow-flip
72×pow1/2
65×frac-2neg clear-num
64×*-commutative
63×pow1/3 frac-times
60×associate-/l/
58×associate-*r/
46×frac-add
43×sqr-pow
37×distribute-rgt-in distribute-lft-in
36×cbrt-div
35×1-exp rec-exp
33×rem-sqrt-square
29×fma-udef
28×exp-prod
27×sum-log
26×tan-quot associate-+r+
25×frac-sub
24×hypot-def
23×div-sub
22×log-div
19×exp-sum +-commutative
18×inv-pow
13×rem-log-exp
12×neg-sub0 associate--l+
11×associate--l-
9×pow-exp pow-pow pow-to-exp
8×exp-diff distribute-rgt-out--
6×pow-div sin-mult
5×sin-sum pow3 hypot-1-def neg-log sub-div un-div-inv
4×expm1-udef exp-neg sqrt-unprod rem-exp-log associate-+l-
3×expm1-log1p cube-unmult sqr-sin
2×log1p-def +.c-commutative hypot-udef unpow1/3 cos-sum tan-sum log1p-udef
1×diff-atan associate-+r- sqrt-undiv frac-2neg.c log1p-expm1 exp-to-pow diff-sin rem-square-sqrt rem-cbrt-cube diff-cos associate--r- expm1-def

localize4.7s (0.7%)

regimes4.5s (0.6%)

Accuracy

Total 22.9b remaining (18.4%)

Threshold costs 5.3b (4.3%)

4.8b83%quadm (p42, negative)
4.8b82.8%quad2m (problem 3.2.1, negative)
3.3b87.6%quad2p (problem 3.2.1, positive)
3.1b-7.4%expq3 (problem 3.4.2)
1.6b86.7%2nthrt (problem 3.4.6)

bsearch2.1s (0.3%)

end1.0ms (0.0%)