Details

simplify19.8m

Calls

11760 calls:

Slowest
1.6s
(/ (* (* (* a c) (* a c)) (* a c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
1.6s
(/ (* (* 1 1) 1) (/ (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* (* (* a c) (* a c)) (* a c))))
1.4s
(/ (* (* (* a a) a) (* (* c c) c)) (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))))
1.4s
(/ (* (* (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* a (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* (* (* a c) (* a c)) (* a c)))
1.3s
(/ (* (* 1 1) 1) (/ (* (* (* a a) a) (* (* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (* (* (* a c) (* a c)) (* a c))))

sample5.0m

Algorithm
56×intervals
16×halfpoints
Results
1.1m66642×body1280valid
38.0s17315×body2560valid
26.8s42415×body640valid
14.6s12557×body10240exit
12.5s94224×body80valid
8.2s20724×body320valid
6.9s63679×body80nan
3.1s10643×body160valid
2.3s47289×pre80true
729.0ms669×body1280nan
543.0ms683×body640nan
477.0ms429×body5120valid
188.0ms366×body320nan
58.0ms198×body160nan

prune2.4m

series34.8s

Calls

385 calls:

Slowest
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
500.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
486.0ms
(- (pow (pow (+ x 1) (/ 1 (* (cbrt n) (cbrt n)))) (/ 1 (cbrt n))) (* (* (cbrt (pow x (/ 1 n))) (cbrt (pow x (/ 1 n)))) (cbrt (pow x (/ 1 n)))))
467.0ms
(sqrt (- (* b b) (* 4 (* a c))))
464.0ms
(- (* -2/5 (pow eps 5)) (* (+ (* (* 2/3 eps) eps) 2) eps))

rewrite12.8s

Algorithm
116×rewrite-expression-head
Calls

385 calls:

Slowest
237.0ms
(* eps (* b (* (* eps b) (* eps b))))
233.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
213.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
194.0ms
(* eps (* b (* (* eps b) (* eps b))))
194.0ms
(* eps (* b (* (* eps b) (* eps b))))
Rules
4717×add-sqr-sqrt
4662×times-frac
4585×*-un-lft-identity
2877×add-cube-cbrt
2431×pow1
1931×add-exp-log
1810×sqrt-prod
1753×add-cbrt-cube
973×difference-of-squares
721×prod-exp
679×add-log-exp
673×pow-prod-down
668×cbrt-unprod
628×associate-*l*
513×pow-prod-up
481×unpow-prod-down
474×associate-/r*
466×distribute-lft-out--
434×cube-prod
375×div-exp
373×insert-posit16
369×associate-/l*
299×cbrt-undiv
297×distribute-lft-out
288×associate-*r*
255×sqr-pow
254×pow-sqr
229×flip3-- flip--
221×div-inv
199×pow-plus
198×associate-*r/
177×flip-+ flip3-+
171×log-prod
169×associate-/r/
164×exp-prod log-pow
151×frac-times
144×sqrt-div
142×pow2
131×swap-sqr cbrt-prod
122×sqrt-pow1
117×unswap-sqr
114×sub-neg
103×pow-unpow associate-*l/ diff-log
92×pow1/2
86×*-commutative
74×tan-quot
71×frac-2neg clear-num
67×associate-/l/
63×frac-sub
62×cbrt-div
58×sum-log
49×distribute-rgt-in distribute-lft-in
42×pow-flip
40×1-exp rec-exp
33×+-commutative
31×pow-pow rem-sqrt-square
29×difference-of-sqr-1 cube-mult associate--l+
28×difference-cubes log-div
26×pow1/3
25×div-sub
19×inv-pow
18×rem-log-exp
16×pow-exp pow-to-exp
13×associate--r+ complex-mul-def frac-add
12×distribute-rgt-neg-in
10×pow-div
associate-+l+
neg-sub0 associate--l- associate-+r+ sqrt-unprod
rem-cube-cbrt unpow3
sin-sum neg-log distribute-lft1-in associate-+l- distribute-rgt-out
exp-diff cube-unmult pow3 sin-mult rem-square-sqrt
*.c-commutative +.c-commutative
cos-mult distribute-rgt-out-- exp-neg sqr-sin frac-2neg-c exp-to-pow rem-exp-log cos-sum tan-sum associate-*l*.c rem-cbrt-cube complex-add-def
diff-atan sin-cos-mult sub0-neg distribute-frac-neg associate-+r- un-div-inv associate-+l+.c diff-sin diff-cos associate--r-

localize5.0s

regimes3.8s

Accuracy

Total 21.2b remaining (13.5%)

6.0b78.2%quad2p (problem 3.2.1, positive)
5.1b43.7%expq3 (problem 3.4.2)
1.6b81.4%2nthrt (problem 3.4.6)
1.2b0%2cos (problem 3.3.5)
1.1b95.4%quadm (p42, negative)

bsearch2.4s

end1.0ms