Details

simplify5.0m (44.1%)

sample4.3m (37.9%)

Algorithm
56×intervals
16×halfpoints
Results
53.2s66642×body1280valid
31.0s17576×body2560valid
21.9s42571×body640valid
10.7s13021×body10240exit
9.0s93739×body80valid
6.0s20711×body320valid
5.4s63589×body80nan
2.0s10639×body160valid
1.7s47423×pre80true
1.0s640×body1280nan
485.0ms646×body640nan
346.0ms478×body5120valid
121.0ms366×body320nan
35.0ms172×body160nan

prune1.1m (9.3%)

series38.5s (5.6%)

Calls

334 calls:

852.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
721.0ms
(* (/ (expm1 (* (* (+ a b) (* (cbrt eps) (cbrt eps))) (cbrt eps))) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
695.0ms
(cbrt x)
587.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
494.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))

rewrite11.1s (1.6%)

Algorithm
113×rewrite-expression-head
Calls

334 calls:

489.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
471.0ms
(* (/ (log1p x) (log1p (- x))) (* (/ (log1p x) (log1p (- x))) (/ (log1p x) (log1p (- x)))))
217.0ms
(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))
196.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
170.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n))))
Rules
6933×*-un-lft-identity
6377×add-sqr-sqrt
6042×times-frac
5056×add-cube-cbrt
3437×prod-diff
1863×pow1
1456×sqrt-prod
1069×add-exp-log
956×add-cbrt-cube
521×distribute-lft-out
517×pow-prod-up
500×add-log-exp
480×difference-of-squares
455×div-inv
387×distribute-lft-out--
386×associate-*r*
374×fma-neg
360×pow-prod-down associate-/r/
331×log1p-expm1-u associate-*l*
328×expm1-log1p-u
326×insert-posit16
292×unpow-prod-down
284×associate-/l*
271×associate-/r*
270×associate-+l+
265×prod-exp
243×cbrt-unprod
242×pow-sqr
240×cbrt-prod
211×pow-plus
200×div-exp
179×log-prod flip-+ flip3-+
160×cbrt-undiv
156×flip3-- flip--
151×pow2
130×distribute-rgt-neg-in
128×pow-unpow unswap-sqr
111×distribute-lft-neg-in
110×associate-*l/
107×fma-def
102×sqrt-div
101×sqr-pow
78×tan-quot
71×frac-times swap-sqr
67×frac-2neg clear-num associate-*r/
64×sqrt-pow1 diff-log
63×*-commutative
62×sub-neg
56×pow1/3
48×pow1/2
41×cbrt-div
40×associate-/l/
37×neg-mul-1
27×sum-log distribute-rgt-in distribute-lft-in rem-sqrt-square
25×pow-flip
24×1-exp rec-exp
23×log-pow
22×+-commutative
21×difference-of-sqr-1 fma-udef
20×div-sub
16×rem-log-exp
15×inv-pow
14×associate-+r+
13×log-div
12×pow-exp frac-sub pow-to-exp
11×expm1-udef frac-add
10×hypot-def
9×sin-mult
8×expm1-log1p neg-sub0
7×associate--l-
6×neg-log pow-pow
5×cos-mult associate--l+
4×cube-unmult associate--r+ un-div-inv
3×sub-div sqr-sin cos-sum distribute-rgt-out-- associate-+l- log1p-udef
2×exp-diff sin-sum associate-+r- frac-2neg.c sin-cos-mult log1p-expm1 pow3 hypot-1-def +.c-commutative log1p-def tan-sum exp-neg rem-cbrt-cube
1×remove-posit16 diff-atan distribute-frac-neg sqrt-unprod exp-prod exp-to-pow hypot-udef sub0-neg rem-exp-log rem-square-sqrt diff-sin diff-cos expm1-def

regimes4.9s (0.7%)

Accuracy

Total 25.6b remaining (20%)

Threshold costs 4.8b (3.8%)

5.0b82.3%quadm (p42, negative)
4.9b82.5%quad2m (problem 3.2.1, negative)
4.6b83.8%quad2p (problem 3.2.1, positive)
3.0b12.6%expq3 (problem 3.4.2)
1.8b91.9%quadp (p42, positive)

localize4.1s (0.6%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)