Details

sample5.0m (40.9%)

Algorithm
56×intervals
16×halfpoints
Results
1.0m66047×body1280valid
38.2s17458×body2560valid
26.3s41614×body640valid
14.0s12441×body10240exit
13.1s94467×body80valid
8.4s20802×body320valid
8.0s63206×body80nan
2.6s11064×body160valid
2.0s47444×pre80true
1.0s657×body640nan
728.0ms698×body1280nan
492.0ms418×body5120valid
226.0ms377×body320nan
93.0ms192×body160nan

simplify4.9m (40.5%)

prune1.4m (11.3%)

series35.6s (4.9%)

Calls

349 calls:

1.2s
(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)))))
619.0ms
(/ (* (expm1 (* (+ a b) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
520.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
504.0ms
(fma (/ (sin x) (* (cos x) (cos x))) (/ (sin x) (* x x)) (- (/ (/ (sin x) (cos x)) x) (fma (/ (sin x) (* x x)) (/ (sin x) (cos x)) (/ (sin x) x))))
483.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))

rewrite8.7s (1.2%)

Algorithm
114×rewrite-expression-head
Calls

349 calls:

256.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
164.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))))
140.0ms
(* (* x x) (* (* x x) (* x x)))
134.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))
132.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
Rules
12865×*-un-lft-identity
12803×times-frac
11617×add-sqr-sqrt
8597×add-cube-cbrt
6061×prod-diff
2384×sqrt-prod
1983×pow1
1499×difference-of-squares
1180×add-exp-log
1081×distribute-lft-out--
1036×add-cbrt-cube
920×distribute-lft-out
866×div-inv
584×fma-neg
558×associate-/r/
539×pow-prod-up
525×add-log-exp
389×associate-/l*
378×pow-prod-down
377×associate-*l*
359×associate-*r*
350×associate-/r*
345×expm1-log1p-u
343×log1p-expm1-u
342×insert-posit16
307×distribute-rgt-neg-in
303×unpow-prod-down
279×prod-exp
271×log-prod
264×div-exp
256×associate-+l+ pow-sqr
255×cbrt-unprod
250×flip3-- flip--
226×pow-plus
213×distribute-lft-neg-in
191×cbrt-prod
181×cbrt-undiv
177×flip-+ flip3-+
161×pow2
128×sqrt-div
126×exp-sum
122×unswap-sqr
117×pow-unpow
98×sqr-pow
83×associate-*l/
75×diff-log
72×sqrt-pow1 frac-2neg clear-num *-commutative
71×neg-mul-1
68×distribute-rgt-in distribute-lft-in
67×fma-def sub-neg
62×pow1/2
51×swap-sqr
46×pow1/3 associate-/l/ associate-*r/
44×log-pow
42×1-exp rec-exp rem-sqrt-square
39×frac-times
36×associate-+r+
29×pow-flip
28×tan-quot
27×fma-udef exp-prod
24×hypot-def
22×sum-log
21×div-sub
18×inv-pow
17×log-div
16×+-commutative
15×cbrt-div
14×frac-sub
13×rem-log-exp
11×pow-pow
10×neg-sub0 pow-exp pow-to-exp
associate--l- difference-of-sqr-1 sin-mult frac-add
neg-log
pow-div distribute-rgt-out--
expm1-udef exp-diff cos-mult associate--l+
expm1-log1p log1p-udef hypot-1-def sqrt-unprod sub-div associate--r+ un-div-inv associate-+l-
associate-+r- log1p-expm1 pow3 sqr-sin cos-sum
sin-sum difference-of-sqr--1 cube-unmult +.c-commutative tan-sum hypot-udef exp-neg log1p-def rem-cbrt-cube
diff-atan frac-2neg.c sin-cos-mult rem-exp-log rem-square-sqrt diff-sin diff-cos expm1-def distribute-rgt-out

localize3.8s (0.5%)

regimes3.5s (0.5%)

Accuracy

Total 26.3b remaining (21%)

Threshold costs 3.9b (3.1%)

5.1b81.2%quad2p (problem 3.2.1, positive)
4.7b82.9%quadm (p42, negative)
4.7b82.9%quad2m (problem 3.2.1, negative)
3.6b86.9%quadp (p42, positive)
3.2b0%expq3 (problem 3.4.2)

bsearch1.3s (0.2%)

end1.0ms (0.0%)