Details

simplify5.2m (42.9%)

sample4.3m (36.0%)

Algorithm
56×intervals
16×halfpoints
Results
48.4s66434×body1280valid
31.9s17570×body2560valid
19.6s42331×body640valid
9.8s12514×body10240exit
7.1s94134×body80valid
6.7s20864×body320valid
6.5s63446×body80nan
2.8s47417×pre80true
1.7s10327×body160valid
655.0ms671×body1280nan
334.0ms492×body5120valid
332.0ms663×body640nan
120.0ms377×body320nan
37.0ms198×body160nan

prune1.3m (10.8%)

series49.6s (6.9%)

Calls

362 calls:

2.3s
(/ (* 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
(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
(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
(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
(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)))))

rewrite13.1s (1.8%)

Algorithm
120×rewrite-expression-head
Calls

362 calls:

829.0ms
(cbrt (* (* (* (cos x) (cos x)) (cos x)) (* (* (* (cos x) (cos x)) (* (cos x) (cos x))) (* (cos x) (cos x)))))
452.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
412.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
304.0ms
(* (* eps (* (* eps b) (* eps b))) b)
219.0ms
(cbrt (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
Rules
7485×*-un-lft-identity
6880×add-sqr-sqrt
6221×times-frac
5338×add-cube-cbrt
3977×prod-diff
1552×pow1
1154×sqrt-prod
1075×add-exp-log
992×add-cbrt-cube
647×difference-of-squares
595×distribute-lft-out--
586×add-log-exp
496×distribute-lft-out
486×div-inv
450×fma-neg
374×pow-prod-down
367×associate-/l*
360×associate-/r/
352×expm1-log1p-u
350×log1p-expm1-u
340×log-prod
322×tan-quot
288×associate-*r*
284×prod-exp
277×associate-*l*
276×pow-prod-up
262×cbrt-unprod
244×frac-times
242×associate-+l+
238×associate-/r*
235×unpow-prod-down
225×flip3-- flip--
215×associate-*l/
204×distribute-rgt-in distribute-lft-in
195×associate-*r/
173×div-exp
172×flip-+ flip3-+
144×sqrt-div
137×cbrt-undiv
134×pow-sqr
130×cube-prod distribute-rgt-neg-in
123×cbrt-prod
114×distribute-lft-neg-in
109×log-pow
104×sub-neg
101×diff-log
94×pow-plus
89×unswap-sqr
88×sqr-pow
86×cbrt-div
72×associate-/l/
70×fma-def
66×frac-2neg pow2 clear-num
64×exp-sum *-commutative
63×exp-prod
55×pow-unpow
52×sqrt-pow1
48×pow1/2
37×fma-udef
36×cos-mult
35×neg-mul-1
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×sum-log pow1/3 frac-sub
17×cube-unmult
16×1-exp rec-exp
15×complex-mul-def
13×+-commutative
8×associate--l- distribute-rgt-out--
7×neg-sub0 exp-diff sub-div associate--r+ hypot-def
6×distribute-neg-in frac-add
5×sin-sum pow-flip pow-exp distribute-frac-neg neg-log pow-pow inv-pow exp-to-pow rem-exp-log pow-to-exp
4×expm1-log1p expm1-udef log1p-expm1 *.c-commutative sqrt-unprod un-div-inv distribute-neg-frac 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 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

regimes5.7s (0.8%)

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)

localize4.8s (0.7%)

bsearch1.3s (0.2%)

end1.0ms (0.0%)