Details

simplify5.6m (44.6%)

sample4.5m (36.1%)

Algorithm
56×intervals
16×halfpoints
Results
50.5s66387×body1280valid
32.8s17053×body2560valid
17.3s42442×body640valid
11.9s12722×body10240exit
10.0s94301×body80valid
5.6s20627×body320valid
4.9s62714×body80nan
2.2s47530×pre80true
2.1s11043×body160valid
1.1s687×body1280nan
345.0ms619×body640nan
342.0ms504×body5120valid
157.0ms375×body320nan
121.0ms199×body160nan

prune1.0m (8.1%)

series57.2s (7.6%)

Calls

369 calls:

1.3s
(/ (* c a) (* (cbrt a) (cbrt (- (sqrt (- (pow b_2 2) (* a c))) b_2))))
1.2s
(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (/ (* (tan x) (sin eps)) (cos eps)) 3))) (fma (fma (/ (tan x) (cos eps)) (sin eps) 1) (/ (* (tan x) (sin eps)) (cos eps)) 1) (- (tan x)))
1.2s
(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
1.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (* eps (+ (* (* 1/2 (pow a 2)) eps) a))) (- (exp (* b eps)) 1.0)))
938.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite17.2s (2.3%)

Algorithm
120×rewrite-expression-head
Calls

369 calls:

596.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
451.0ms
(+ (/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))
287.0ms
(* (/ (+ 0 (* c (* 4.0 a))) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
279.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
269.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
Rules
9973×*-un-lft-identity
9520×times-frac
8957×add-sqr-sqrt
7081×add-cube-cbrt
4278×prod-diff
3211×sqrt-prod
1179×unpow-prod-down
1139×add-exp-log
934×add-cbrt-cube
891×difference-of-squares
883×distribute-lft-out
639×pow1
629×associate-*l*
584×distribute-lft-out--
579×add-log-exp
573×associate-/l*
524×fma-neg
519×div-inv
417×sqr-pow
402×associate-*r*
400×associate-/r/
360×expm1-log1p-u
357×log1p-expm1-u
356×associate-/r*
309×distribute-rgt-neg-in
306×cbrt-prod
291×distribute-lft-neg-in
256×prod-exp
251×div-exp
247×associate-+l+
240×flip-- flip3--
216×cube-prod
210×log-prod
190×cbrt-undiv
176×cbrt-unprod
160×flip-+ flip3-+
141×unswap-sqr
129×exp-sum
118×sqrt-div
107×fma-def
101×swap-sqr
97×sub-neg neg-mul-1
93×diff-log
81×log-pow
78×associate-/l/ frac-2neg clear-num
76×pow-prod-down
74×sqrt-pow1
67×associate-*l/
65×unpow2
64×pow1/2
54×pow-unpow
49×associate-*r/
48×*-commutative
44×distribute-rgt-in distribute-lft-in
41×pow1/3
40×unpow3
37×div-sub
36×pow-exp
35×cube-mult
34×tan-quot
33×pow-to-exp
32×rem-sqrt-square
31×cbrt-div frac-times
28×fma-udef
26×log-div
20×pow-flip sum-log 1-exp rec-exp
19×exp-prod
15×pow-prod-up +-commutative associate--l+ rem-log-exp
13×frac-add complex-mul-def
12×pow-pow frac-sub
11×pow-sqr neg-sub0
10×pow-div distribute-rgt-out--
7×rem-cube-cbrt associate-+l-
6×inv-pow associate--r+ expm1-udef
5×sin-cos-mult difference-cubes log1p-udef associate--l- log1p-expm1 pow2 expm1-log1p pow-plus
4×exp-diff sqrt-unprod *.c-commutative hypot-def neg-log
3×cube-div exp-neg +.c-commutative distribute-frac-neg
2×un-div-inv sub-div complex-add-def rem-square-sqrt sqrt-undiv cos-sum sin-mult tan-sum frac-2neg.c sin-sum
1×rem-exp-log associate-+l+.c associate-+r- diff-atan diff-cos hypot-udef associate-*l*.c rem-cbrt-cube exp-to-pow diff-sin

regimes4.2s (0.6%)

Accuracy

Total 27.3b remaining (21.6%)

Threshold costs 7.3b (5.8%)

4.7b83.5%quadp (p42, positive)
4.5b84.2%quad2p (problem 3.2.1, positive)
3.3b87.9%quad2m (problem 3.2.1, negative)
3.1b88.3%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)

localize4.1s (0.5%)

bsearch2.1s (0.3%)

end1.0ms (0.0%)