Details

simplify5.2m (42.4%)

sample4.4m (36.3%)

Algorithm
56×intervals
16×halfpoints
Results
50.6s66434×body1280valid
33.9s17570×body2560valid
19.5s42331×body640valid
8.8s12514×body10240exit
7.6s94134×body80valid
6.6s20864×body320valid
5.0s63446×body80nan
2.2s10327×body160valid
1.4s671×body1280nan
1.3s47417×pre80true
365.0ms492×body5120valid
363.0ms663×body640nan
116.0ms377×body320nan
38.0ms198×body160nan

prune1.3m (10.6%)

series51.4s (7.1%)

Calls

361 calls:

2.2s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* (* eps (* (* eps b) (* eps b))) b) 1/6 (fma (* (* eps b) (* eps b)) 1/2 (* eps b)))))
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)))))
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))))
1.1s
(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)))))

rewrite13.3s (1.8%)

Algorithm
120×rewrite-expression-head
Calls

361 calls:

777.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
713.0ms
(cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x)))))
408.0ms
(* (* x x) 1/3)
276.0ms
(* (* eps (* (* eps b) (* eps b))) b)
218.0ms
(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
Rules
7524×*-un-lft-identity
6921×add-sqr-sqrt
6216×times-frac
5371×add-cube-cbrt
4037×prod-diff
1554×pow1
1183×sqrt-prod
1077×add-exp-log
994×add-cbrt-cube
653×difference-of-squares
601×distribute-lft-out--
587×add-log-exp
493×distribute-lft-out
486×div-inv
460×fma-neg
376×pow-prod-down
362×associate-/l*
360×associate-/r/
351×expm1-log1p-u
349×log1p-expm1-u
340×log-prod
322×tan-quot
288×associate-*r*
286×prod-exp
276×pow-prod-up
275×associate-*l*
264×cbrt-unprod
248×frac-times
242×associate-+l+
238×associate-/r*
235×unpow-prod-down
230×flip3-- flip--
217×associate-*l/
204×distribute-rgt-in distribute-lft-in
201×associate-*r/
174×flip-+ flip3-+
173×div-exp
154×sqrt-div
146×distribute-rgt-neg-in
137×cbrt-undiv
134×pow-sqr
130×cube-prod
127×distribute-lft-neg-in
125×cbrt-prod
109×log-pow
105×sub-neg
103×diff-log
94×pow-plus
90×cbrt-div
88×sqr-pow
87×unswap-sqr
72×associate-/l/
66×frac-2neg pow2 clear-num
64×exp-sum *-commutative fma-def
63×exp-prod
55×pow-unpow
52×sqrt-pow1
48×pow1/2
40×neg-mul-1
36×cos-mult fma-udef
32×div-sub
31×unpow3 cube-mult
30×rem-sqrt-square
28×associate-+r+
27×log-div
22×swap-sqr rem-log-exp
20×associate--l+
18×pow1/3 frac-sub
17×sum-log cube-unmult
16×1-exp rec-exp
15×complex-mul-def
12×+-commutative
9×associate--l-
8×distribute-rgt-out--
7×neg-sub0 exp-diff sub-div associate--r+ hypot-def
6×neg-log distribute-neg-in frac-add
5×sin-sum pow-flip pow-exp pow-pow inv-pow exp-to-pow rem-exp-log pow-to-exp
4×expm1-log1p expm1-udef log1p-expm1 *.c-commutative distribute-frac-neg sqrt-unprod un-div-inv pow-div log1p-udef
3×pow3 sin-mult +.c-commutative associate-+l- cos-sum difference-cubes
2×frac-2neg.c distribute-rgt-neg-out complex-def-add distribute-neg-frac sqr-cos tan-sum rem-cbrt-cube associate-*l*.c complex-add-def
1×diff-atan rem-cube-cbrt sin-cos-mult associate-+r- distribute-lft-in.c rem-square-sqrt distribute-rgt-in.c diff-sin associate-+l+.c diff-cos +-inverses

regimes6.3s (0.9%)

Accuracy

Total 23.8b remaining (18.6%)

Threshold costs 7.1b (5.5%)

4.6b84%quadp (p42, positive)
4.5b84.5%quad2p (problem 3.2.1, positive)
4.3b85%quadm (p42, negative)
2.3b74.1%2nthrt (problem 3.4.6)
1.0b95.7%quad2m (problem 3.2.1, negative)

localize5.2s (0.7%)

bsearch1.4s (0.2%)

end1.0ms (0.0%)