Details

simplify13.4m

Calls

10190 calls:

Slowest
1.6s
(re (+.c (+.c (+.c (+.c (+.c (+.c (*.c (*.c (*.c (*.c (*.c (complex -1 1) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (*.c (*.c (*.c (*.c (*.c (complex 6 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (*.c (complex 20 0) (complex -1 1)) (complex -1 1)) (complex -1 1))) (*.c (*.c (complex 15 0) (complex -1 1)) (complex -1 1))) (*.c (complex 6 0) (complex -1 1))) (complex 1 0)))
1.4s
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* (* x x) (* x x)) (* x x)))
1.4s
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
1.4s
(* (* (* (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps))))) (* (cos x) (cos x))) (+ (* (/ (/ (sin eps) (cos eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps))))))) (- (* (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps))))))) (* (/ (/ (sin eps) (cos eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))))))) (cos x))
1.4s
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin x) (sin x)) (sin x))) (* (* (* (* x x) (+ 1 (cos x))) (* (* x x) (+ 1 (cos x)))) (* (* x x) (+ 1 (cos x)))))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67191×body1280valid
40.1s17659×body2560valid
26.2s42009×body640valid
14.1s13066×body10240exit
11.0s93742×body80valid
8.6s20392×body320valid
7.3s63223×body80nan
2.6s10774×body160valid
2.5s47486×pre80true
944.0ms639×body640nan
649.0ms635×body1280nan
641.0ms502×body5120valid
155.0ms332×body320nan
82.0ms212×body160nan

prune2.2m

series37.9s

Calls

387 calls:

Slowest
1.9s
(- (* (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ 1 (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (tan x))
1.2s
(* (cbrt x) (- 1/9 (* (/ -1/9 x) (/ -1/9 x))))
1.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
1.0s
(- (+ (* (/ (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ (/ (/ (sin eps) (cos eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))))) (/ (sin x) (cos x)))
566.0ms
(* (/ (cbrt x) x) (+ 1/3 (/ -1/9 x)))

rewrite19.2s

Algorithm
118×rewrite-expression-head
Calls

387 calls:

Slowest
3.7s
(* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1))
2.6s
(- (+ (* (/ (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps))) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))) (+ (/ (/ (sin eps) (cos eps)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (/ (sin eps) (cos eps)))))))) (/ (sin x) (cos x)))
783.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
424.0ms
(- (log (+ N 1)) (log N))
202.0ms
(* (+ (sqrt (pow x -1/2)) (sqrt (log (exp (/ 1 (sqrt (+ x 1))))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
Rules
3999×add-sqr-sqrt
3966×*-un-lft-identity
3834×times-frac
2612×add-cube-cbrt
2088×pow1
1362×add-exp-log
1222×add-cbrt-cube
1064×sqrt-prod
685×add-log-exp
644×associate-*l*
539×pow-prod-down
509×difference-of-squares
467×pow-prod-up
409×prod-exp
400×associate-*r*
397×distribute-lft-out
383×cbrt-unprod
376×insert-posit16
368×associate-/l*
334×associate-/r*
276×unpow-prod-down
270×log-prod
255×distribute-lft-out--
245×div-inv
230×pow-sqr
222×div-exp
203×pow-plus
193×cbrt-prod
180×flip-+ flip3-+
169×flip3-- flip--
160×cbrt-undiv
148×exp-prod
144×swap-sqr unswap-sqr
134×pow2
127×frac-times
115×cube-prod
110×log-pow
105×sub-neg
100×diff-log
99×sqr-pow
98×associate-/r/
96×associate-*r/
95×*-commutative associate-*l/
74×pow-unpow
73×sqrt-div
69×cbrt-div
68×frac-2neg clear-num
66×associate-/l/
59×sum-log tan-quot
52×frac-add
50×sqrt-pow1 frac-sub
44×pow1/2
41×pow1/3
38×distribute-rgt-in +-commutative distribute-lft-in
35×pow-flip
34×exp-sum
30×1-exp rec-exp cube-mult
29×rem-log-exp
27×sum-cubes
25×log-div
24×distribute-rgt-neg-in
23×rem-sqrt-square
19×difference-of-sqr-1
18×pow-exp inv-pow div-sub
17×pow-to-exp
16×associate--l+
15×associate--r+ pow-pow
13×complex-mul-def
10×associate-+l+ associate--l-
neg-sub0 distribute-rgt-out--
associate-+r+ rem-exp-log
sin-sum distribute-lft1-in exp-to-pow distribute-rgt-out
rem-cube-cbrt neg-log sin-mult associate-+l-
exp-diff cos-mult *.c-commutative unpow3 sub-div +.c-commutative sqr-cos cube-div distribute-lft-neg-in
associate-*l*.c pow3 sqrt-unprod sqr-sin tan-sum exp-neg rem-square-sqrt cos-sum complex-add-def
diff-atan associate-+r- sin-cos-mult neg-mul-1 frac-2neg-c diff-sin associate-+l+.c rem-cbrt-cube diff-cos associate--r-

regimes5.7s

Accuracy

Total 26.5b remaining (21.8%)

4.7b83.4%quad2p (problem 3.2.1, positive)
4.7b83.4%quadp (p42, positive)
4.1b85.6%quad2m (problem 3.2.1, negative)
3.3b0%expq3 (problem 3.4.2)
2.8b74.9%2nthrt (problem 3.4.6)

localize5.1s

bsearch1.9s

end1.0ms