Details

simplify9.4m (45.9%)

sample5.1m (24.7%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67223×body1280valid
39.5s17247×body2560valid
26.8s42743×body640valid
14.5s12792×body10240exit
10.8s94155×body80valid
8.6s20240×body320valid
7.8s63595×body80nan
2.5s10190×body160valid
2.1s47494×pre80true
742.0ms660×body1280nan
518.0ms647×body640nan
507.0ms452×body5120valid
261.0ms434×body320nan
98.0ms184×body160nan

prune5.0m (24.4%)

series37.6s (3.1%)

Calls

353 calls:

990.0ms
(- (/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
917.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
512.0ms
(fma (/ -1 (sqrt (cbrt (+ x 1)))) (/ 1 (fabs (cbrt (+ x 1)))) (/ (/ 1 (fabs (cbrt (+ x 1)))) (sqrt (cbrt (+ x 1)))))
474.0ms
(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))
465.0ms
(/ (* x (fma (* (* (* x x) 1/45) (* (* x x) 1/45)) (* (* x x) 1/45) 1/27)) (+ (* (* x (* x 1/45)) (* x (* x 1/45))) (- (* 1/3 1/3) (* (* x (* x 1/45)) 1/3))))

rewrite12.9s (1.0%)

Algorithm
116×rewrite-expression-head
Calls

353 calls:

1.9s
(- (/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))) (/ (* (/ 1 (- x 1)) (/ 1 (- x 1))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))))
480.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
424.0ms
(/ (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))
292.0ms
(* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x)))
280.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (cos x) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
Rules
29858×times-frac
24738×add-sqr-sqrt
22053×*-un-lft-identity
14207×add-cube-cbrt
9922×prod-diff
3634×difference-of-squares
3347×sqrt-prod
1939×distribute-lft-out--
1931×div-inv
1868×pow1
1347×distribute-lft-out
1179×add-exp-log
974×add-cbrt-cube
844×associate-/r/
736×distribute-rgt-in distribute-lft-in
735×fma-neg
690×associate-/r*
581×associate-+l+
570×log-prod
523×add-log-exp
521×pow-prod-up
497×associate--l+
448×frac-sub
392×unpow-prod-down
389×associate-/l*
374×flip3-- flip--
349×expm1-log1p-u
347×log1p-expm1-u
345×insert-posit16
340×associate-*l*
335×pow-prod-down
329×cbrt-prod
296×div-exp
264×associate-*r*
259×flip-+ flip3-+
243×prod-exp
220×pow-sqr
215×pow-plus
211×cbrt-unprod
190×associate-+r+
184×cbrt-undiv
153×frac-times
152×distribute-rgt-neg-in
151×sqr-pow
145×pow2
141×sqrt-div
136×associate-/l/
132×swap-sqr
126×distribute-lft-neg-in
114×associate-*l/
101×unswap-sqr
89×associate-*r/
83×sub-neg
80×sqrt-pow1
79×diff-log
78×pow-unpow
76×frac-2neg clear-num
75×fma-def
71×pow1/3
66×log-pow
63×*-commutative
59×pow1/2
54×cbrt-div
53×1-exp rec-exp
47×pow-flip
42×neg-mul-1
34×rem-sqrt-square
33×un-div-inv
29×inv-pow
27×tan-quot difference-of-sqr-1 log-div
23×exp-prod
21×fma-udef
20×div-sub hypot-def
17×associate--r+
16×sum-log
13×+-commutative rem-log-exp
12×associate--l- frac-add
10×sin-mult
8×neg-sub0 pow-exp
7×distribute-rgt-out-- log1p-udef pow-to-exp log1p-def
6×pow-div pow3 neg-log pow-pow associate-+l-
5×cos-mult sqr-sin associate--r-
4×log1p-expm1 rem-exp-log
3×expm1-log1p expm1-udef sub-div cos-sum
2×exp-diff sin-sum frac-2neg.c cube-unmult +.c-commutative tan-sum exp-neg
1×diff-atan associate-+r- sqrt-undiv sin-cos-mult sqrt-unprod hypot-udef exp-to-pow rem-square-sqrt +-inverses diff-sin diff-cos expm1-def e-exp-1

localize4.4s (0.4%)

regimes4.4s (0.4%)

Accuracy

Total 24.4b remaining (17.4%)

Threshold costs 6.1b (4.3%)

5.5b80%quadm (p42, negative)
4.2b85%quadp (p42, positive)
4.2b85.2%quad2p (problem 3.2.1, positive)
2.9b9.4%expq3 (problem 3.4.2)
1.5b87.7%2nthrt (problem 3.4.6)

bsearch2.0s (0.2%)

end1.0ms (0.0%)