Details

sample5.0m (33.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67429×body1280valid
39.0s17389×body2560valid
26.7s41851×body640valid
12.9s12829×body10240exit
11.7s93836×body80valid
7.9s20701×body320valid
7.2s63522×body80nan
2.5s10486×body160valid
2.3s47295×pre80true
657.0ms680×body1280nan
532.0ms685×body640nan
498.0ms489×body5120valid
210.0ms378×body320nan
47.0ms175×body160nan

simplify4.7m (31.8%)

prune4.2m (28.3%)

series38.1s (4.3%)

Calls

356 calls:

838.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
655.0ms
(cbrt (fma (* -4 c) a (* b b)))
572.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
571.0ms
(fma (sqrt (* (cbrt (fma (* -4 c) a (* b b))) (cbrt (fma (* -4 c) a (* b b))))) (sqrt (cbrt (fma (* -4 c) a (* b b)))) b)
532.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite8.3s (0.9%)

Algorithm
114×rewrite-expression-head
Calls

356 calls:

445.0ms
(+ (* 1/45 (* x x)) 1/3)
186.0ms
(/ (* x (fma (* (* x (* x 1/45)) (* x (* x 1/45))) (* x (* x 1/45)) 1/27)) (+ (* (* 1/45 (* x x)) (* 1/45 (* x x))) (- (* 1/3 1/3) (* (* 1/45 (* x x)) 1/3))))
175.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
173.0ms
(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))
161.0ms
(/ (- (/ (pow x -1/2) x) (/ (/ 1 (+ x 1)) (sqrt (+ x 1)))) (+ (/ 1 (+ x 1)) (fma (pow x -1/2) (pow x -1/2) (/ (pow x -1/2) (sqrt (+ x 1))))))
Rules
19445×times-frac
15675×*-un-lft-identity
14034×add-sqr-sqrt
11879×add-cube-cbrt
7556×prod-diff
4246×sqrt-prod
2675×pow1
1816×unpow-prod-down
1509×distribute-lft-out
1261×add-exp-log
1068×div-inv
1063×add-cbrt-cube
911×pow-prod-up
689×difference-of-squares
671×associate-/r/
666×sqr-pow
628×cbrt-prod
507×add-log-exp
502×associate-*l*
499×pow-prod-down
453×fma-neg
435×associate-/l*
392×flip-+ flip3-+
386×associate-*r*
375×sqrt-div
372×pow-sqr
362×distribute-rgt-neg-in
355×associate-/r*
353×expm1-log1p-u log1p-expm1-u
349×insert-posit16
335×pow-plus
327×distribute-lft-neg-in
300×div-exp
298×distribute-lft-out--
297×prod-exp
292×associate-+l+
267×pow-unpow
257×cbrt-unprod
237×pow2
221×sqrt-pow1
197×cbrt-undiv
193×unswap-sqr
160×log-prod
148×flip3-- flip--
127×associate-*l/
126×cube-prod
109×neg-mul-1
104×pow1/2
103×swap-sqr
83×frac-times
77×pow1/3
76×frac-2neg clear-num
75×fma-def
68×*-commutative
63×sub-neg
61×associate-*r/
58×diff-log
54×distribute-rgt-in distribute-lft-in
52×pow-flip
47×1-exp rec-exp associate-/l/
42×frac-add
35×fma-udef
33×inv-pow rem-sqrt-square
32×tan-quot
25×sum-log
24×frac-sub pow-div div-sub
23×cbrt-div log-pow
21×exp-prod
18×+-commutative
15×difference-of-sqr-1
13×pow-exp pow-to-exp
11×pow-pow
10×cube-unmult hypot-def
9×neg-sub0 expm1-udef log1p-udef
8×associate--l- rem-log-exp
7×associate--r+ difference-cubes cube-mult un-div-inv
6×log-div
5×expm1-log1p log1p-expm1
4×associate-+r+ neg-log sqrt-unprod sub-div sin-mult
3×sin-sum exp-sum sqr-sin rem-exp-log
2×quot-tan exp-diff log1p-def sin-cos-mult pow3 +.c-commutative tan-sum exp-to-pow exp-neg distribute-rgt-out-- associate-+l- cos-sum
1×distribute-lft1-in diff-atan cos-mult associate--l+ frac-2neg-c hypot-udef rem-square-sqrt diff-sin sqr-cos diff-cos expm1-def distribute-rgt-out

regimes4.8s (0.5%)

Accuracy

Total 27.6b remaining (18.3%)

Threshold costs 6.2b (4.1%)

6.2b81.7%quadm (p42, negative)
4.9b-45.4%expq3 (problem 3.4.2)
4.6b84%quad2m (problem 3.2.1, negative)
4.4b84.2%quad2p (problem 3.2.1, positive)
1.3b89.3%2nthrt (problem 3.4.6)

localize4.3s (0.5%)

bsearch2.9s (0.3%)

end1.0ms (0.0%)