Details

simplify12.1m

Calls

9927 calls:

Slowest
1.7s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) x) (- x 1)) (* (* (+ x 1) x) (- x 1))) (* (* (+ x 1) x) (- x 1))))
1.4s
(/ (* (* (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1)) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (+ (* (- (* 1 x) (* (+ x 1) 2)) (- x 1)) (* (* (+ x 1) x) 1))) (* (* (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* x x) x)) (* (* (- x 1) (- x 1)) (- x 1))))
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)))))
1.2s
(/ (* (* (* (sin x) (sin x)) (* (sin x) (sin x))) (* (sin x) (sin x))) (* (* (* (* x x) x) (* (* x x) x)) (* (* (+ 1 (cos x)) (+ 1 (cos x))) (+ 1 (cos x)))))
1.2s
(im (+.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)))

sample5.1m

Algorithm
56×intervals
16×halfpoints
Results
1.1m67025×body1280valid
39.7s17549×body2560valid
26.5s41666×body640valid
14.2s12910×body10240exit
11.8s93927×body80valid
9.5s21014×body320valid
6.5s62901×body80nan
3.6s10717×body160valid
2.7s47530×pre80true
899.0ms658×body640nan
709.0ms631×body1280nan
536.0ms467×body5120valid
209.0ms369×body320nan
71.0ms192×body160nan

prune2.3m

series39.8s

Calls

386 calls:

Slowest
2.0s
(- (* (/ (+ (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))
1.7s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
667.0ms
(cbrt x)
611.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
562.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite12.7s

Algorithm
119×rewrite-expression-head
Calls

386 calls:

Slowest
522.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
347.0ms
(* (* (* (* x x) (* x x)) (* x x)) 1/360)
256.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
251.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
204.0ms
(* eps (* b (* (* eps b) (* eps b))))
Rules
3727×*-un-lft-identity
3641×add-sqr-sqrt
3520×times-frac
2552×add-cube-cbrt
1849×sqrt-prod
1617×pow1
1481×add-exp-log
1306×add-cbrt-cube
712×associate-*l*
633×add-log-exp
494×prod-exp
467×pow-prod-down
437×cbrt-unprod
422×associate-*r*
375×insert-posit16
360×associate-/l*
358×distribute-lft-out
351×difference-of-squares
319×cbrt-prod
302×associate-/r*
238×distribute-lft-out--
234×div-exp
224×log-prod
213×div-inv
209×flip3-- flip--
204×associate-*l/
201×log-pow
185×flip-+ flip3-+
172×cbrt-undiv
161×swap-sqr
152×pow-prod-up
141×associate-/r/
140×unswap-sqr
130×sqrt-div
126×associate-*r/
118×sqrt-pow1
113×frac-times
106×pow-sqr
105×sub-neg
98×pow-unpow pow1/2
95×*-commutative
93×unpow-prod-down
91×diff-log
80×associate-/l/
72×pow-plus
70×frac-2neg clear-num
64×tan-quot
59×distribute-rgt-neg-in
58×exp-prod
57×pow1/3
55×distribute-rgt-out
54×pow2
53×cbrt-div
49×distribute-rgt-in distribute-lft-in
45×log-div
44×sum-log
43×pow-flip frac-add
37×1-exp rec-exp distribute-lft-neg-in
33×sqr-pow
31×associate--l+
30×difference-of-sqr-1
29×frac-sub +-commutative rem-log-exp
24×rem-sqrt-square
20×cube-prod
19×div-sub
17×inv-pow
16×associate--r+ pow-pow
15×distribute-lft1-in
14×pow-exp
13×complex-mul-def pow-to-exp
11×associate--l-
10×pow-div distribute-rgt1-in
associate-+l+ neg-sub0
neg-log
neg-mul-1
exp-sum distribute-rgt-out-- associate-+l- cube-mult
sin-sum sqrt-unprod
associate-+r+ sin-mult sub-div sum-cubes un-div-inv
rem-cube-cbrt *.c-commutative +.c-commutative cube-div
exp-diff associate-*l*.c associate-+r- unpow3 sqr-sin complex-add-def rem-square-sqrt cos-sum tan-sum e-exp-1
remove-posit16 diff-atan cos-mult sin-cos-mult pow3 log-rec distribute-frac-neg frac-2neg-c distribute-neg-frac associate-+l+.c diff-sin diff-cos rem-cbrt-cube

localize4.7s

regimes4.3s

Accuracy

Total 25.9b remaining (20.8%)

4.8b82.9%quadp (p42, positive)
4.7b83.4%quad2p (problem 3.2.1, positive)
4.3b37.5%2tan (problem 3.3.2)
3.3b0%expq3 (problem 3.4.2)
2.0b78.1%2nthrt (problem 3.4.6)

bsearch2.4s

end1.0ms