Details

simplify4.9m (39.8%)

sample4.9m (39.8%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m67113×body1280valid
36.8s17237×body2560valid
25.3s42016×body640valid
14.9s12757×body10240exit
11.6s93998×body80valid
8.6s20566×body320valid
6.7s62518×body80nan
2.9s10871×body160valid
2.0s47509×pre80true
633.0ms647×body1280nan
600.0ms708×body640nan
511.0ms438×body5120valid
212.0ms362×body320nan
48.0ms187×body160nan

prune1.5m (12.5%)

series38.1s (5.1%)

Calls

356 calls:

630.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
583.0ms
(/ (* (expm1 (* (+ a b) eps)) (/ eps (expm1 (* eps a)))) (expm1 (* eps b)))
542.0ms
(- (pow (+ 1 x) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
525.0ms
(- (tan (+ x eps)) (tan x))
524.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))

rewrite9.5s (1.3%)

Algorithm
114×rewrite-expression-head
Calls

356 calls:

341.0ms
(/ (/ (- (+ x 1) x) (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
245.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
187.0ms
(* (* (* eps eps) (* eps (* eps eps))) -2/5)
170.0ms
(* (* (* eps eps) (* eps (* eps eps))) -2/5)
167.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (/ (sin eps) (cos x)) (sin x)) (cos eps)))) (/ (sin x) (cos x)))
Rules
12963×times-frac
12409×*-un-lft-identity
10896×add-sqr-sqrt
8436×add-cube-cbrt
6375×prod-diff
2658×pow1
2381×sqrt-prod
1378×add-exp-log
1242×add-cbrt-cube
1231×difference-of-squares
1012×distribute-lft-out
976×div-inv
833×distribute-lft-out--
827×pow-prod-up
590×fma-neg
574×associate-/r/
559×add-log-exp
538×pow-prod-down
422×prod-exp
385×cbrt-unprod
381×associate-*l*
359×associate-/l*
357×pow-sqr
352×log1p-expm1-u
350×expm1-log1p-u
349×insert-posit16
332×pow-plus
299×distribute-rgt-neg-in
291×associate-*r*
285×flip3-- flip--
276×associate-+l+
270×distribute-lft-neg-in
268×div-exp associate-/r*
262×associate-+r+
260×sqrt-div
259×cbrt-prod
233×pow2
225×flip-+ flip3-+
223×cbrt-undiv
198×log-prod
142×associate-*l/
128×pow-unpow unpow-prod-down
120×fma-def
114×unswap-sqr
108×log-pow
90×neg-mul-1
89×swap-sqr
83×diff-log
80×sub-neg
70×sqrt-pow1
67×pow1/2
65×frac-2neg clear-num *-commutative
64×pow-flip
63×pow1/3 frac-times
60×associate-/l/ associate-*r/
49×exp-prod frac-add
41×sqr-pow
38×distribute-rgt-in distribute-lft-in
36×cbrt-div
33×rem-sqrt-square
32×1-exp rec-exp
30×fma-udef
29×sum-log
26×tan-quot
24×hypot-def
23×div-sub
22×log-div
21×frac-sub
20×+-commutative
19×exp-sum
18×difference-of-sqr-1
15×inv-pow
14×rem-log-exp
12×neg-sub0 associate--r+ associate--l+
11×associate--l-
9×pow-pow
8×exp-diff pow-exp pow-to-exp
6×sin-mult
5×sin-sum neg-log hypot-1-def un-div-inv distribute-rgt-out--
4×expm1-udef cube-unmult exp-neg pow3 sqrt-unprod sub-div rem-exp-log associate-+l-
3×expm1-log1p sqr-sin
2×associate-+r- log1p-def hypot-udef unpow1/3 cos-sum tan-sum +.c-commutative log1p-udef
1×diff-atan sqrt-undiv frac-2neg.c log1p-expm1 exp-to-pow diff-sin rem-square-sqrt rem-cbrt-cube diff-cos expm1-def

regimes4.5s (0.6%)

Accuracy

Total 22.9b remaining (18.4%)

Threshold costs 5.3b (4.3%)

4.8b83%quadm (p42, negative)
4.8b82.8%quad2m (problem 3.2.1, negative)
3.3b87.6%quad2p (problem 3.2.1, positive)
3.1b-7.4%expq3 (problem 3.4.2)
1.6b86.7%2nthrt (problem 3.4.6)

localize4.2s (0.6%)

bsearch2.7s (0.4%)

end1.0ms (0.0%)