Details

simplify4.8m (39.8%)

sample4.3m (35.0%)

Algorithm
56×intervals
16×halfpoints
Results
49.4s66434×body1280valid
30.9s17570×body2560valid
17.9s42331×body640valid
9.9s12514×body10240exit
8.7s94134×body80valid
5.6s20864×body320valid
5.0s63446×body80nan
2.1s10327×body160valid
1.5s47417×pre80true
599.0ms671×body1280nan
430.0ms663×body640nan
322.0ms492×body5120valid
168.0ms377×body320nan
36.0ms198×body160nan

prune1.7m (13.8%)

series55.2s (7.6%)

Calls

373 calls:

2.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* (* eps b) (* eps b)) 1/2 (fma 1/6 (* eps (* (* (* eps b) (* eps b)) b)) (* eps b)))))
1.6s
(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
1.2s
(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.2s
(expm1 (log1p (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))
1.2s
(fma (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n))) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))

rewrite13.4s (1.8%)

Algorithm
120×rewrite-expression-head
Calls

373 calls:

496.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))
472.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ 1.0 (sqrt (+ x 1.0)))))
384.0ms
(tan (+ x eps))
367.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
324.0ms
(/ (- (* (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x))) (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt x)))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ (* (sqrt 1.0) (/ (sqrt 1.0) (sqrt (cbrt x)))) (fabs (cbrt (* (* (cbrt x) (cbrt x)) (cbrt x))))) (/ 1.0 (sqrt (+ x 1.0)))))
Rules
10884×times-frac
10523×add-sqr-sqrt
10270×*-un-lft-identity
7703×add-cube-cbrt
5557×prod-diff
2395×sqrt-prod
1287×difference-of-squares
1226×add-exp-log
1106×add-cbrt-cube
998×pow1
759×div-inv
694×associate-*l*
668×distribute-lft-out--
614×add-log-exp
560×fma-neg
448×distribute-lft-out
400×associate-/r/
372×associate-/l*
363×log1p-expm1-u
362×expm1-log1p-u
344×prod-exp
305×cbrt-unprod
281×flip3-- flip--
263×distribute-rgt-in distribute-lft-in
257×associate-*r*
251×unpow-prod-down
248×associate-/r*
243×associate-+l+
242×pow-prod-down
237×cbrt-prod
222×div-exp
180×cbrt-undiv
174×flip-+ flip3-+
169×log-prod
162×distribute-rgt-neg-in
150×associate-*l/
140×cube-prod
136×distribute-lft-neg-in
130×sqrt-div
112×frac-times
111×fma-def
107×diff-log
105×sub-neg
104×cbrt-div
94×sqr-pow
93×unswap-sqr
84×associate-/l/
82×associate-*r/
76×sqrt-pow1 pow-prod-up
70×frac-2neg clear-num
69×log-pow
63×pow-unpow
59×*-commutative
53×frac-sub
50×swap-sqr
48×pow1/3 pow1/2
44×neg-mul-1
41×fma-udef
40×associate-+r+
38×pow-plus pow-sqr
34×unpow3 cube-mult
27×div-sub
26×tan-quot
25×associate--l+ pow2
24×rem-sqrt-square
23×sum-log
21×log-div
19×pow-flip 1-exp rec-exp
17×rem-log-exp
15×+-commutative
14×complex-mul-def
13×exp-prod frac-add
12×pow-div
11×associate--l-
pow-exp
neg-sub0 neg-log associate--r+ distribute-neg-in
pow-pow pow-to-exp
distribute-rgt-out-- exp-sum unpow-prod-up
cos-mult distribute-rgt-neg-out sub-div inv-pow exp-to-pow distribute-neg-frac rem-exp-log sin-mult
quot-tan hypot-def log1p-udef
expm1-log1p expm1-udef associate-+r- cube-unmult *.c-commutative distribute-frac-neg +.c-commutative un-div-inv associate-+l- difference-cubes
sin-sum sin-cos-mult log1p-expm1 pow3 frac-2neg.c tan-sum associate-*l*.c cos-sum unsub-neg e-exp-1 complex-add-def
diff-atan rem-cube-cbrt sqrt-unprod rem-square-sqrt diff-sin sqr-cos +-inverses associate-+l+.c diff-cos

regimes6.9s (0.9%)

Accuracy

Total 24.1b remaining (15.1%)

Threshold costs 6.0b (3.8%)

4.7b83.9%quadp (p42, positive)
4.4b84.5%quad2p (problem 3.2.1, positive)
4.0b86.1%quad2m (problem 3.2.1, negative)
2.4b74.1%2nthrt (problem 3.4.6)
1.6b84.3%2cos (problem 3.3.5)

localize5.7s (0.8%)

bsearch1.5s (0.2%)

end1.0ms (0.0%)