Details

sample2.7m (41.4%)

Algorithm
55×intervals
16×halfpoints
Results
33.4s66384×body1280valid
21.5s16192×body2560valid
11.7s41362×body640valid
6.5s12621×body10240exit
4.3s87973×body80valid
3.7s20423×body320valid
3.0s60483×body80nan
1.1s10867×body160valid
800.0ms47432×pre80true
348.0ms647×body1280nan
236.0ms642×body640nan
160.0ms347×body5120valid
93.0ms342×body320nan
22.0ms175×body160nan

simplify2.3m (34.8%)

prune32.9s (8.5%)

series32.5s (8.3%)

Calls

386 calls:

905.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
822.0ms
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (* (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n))))) (pow x (/ 1.0 n)))
821.0ms
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (* (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (sqrt (pow (cbrt (+ x 1.0)) (/ 1.0 n))))) (pow x (/ 1.0 n)))
814.0ms
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))
497.0ms
(cbrt (cbrt x))

rewrite20.6s (5.3%)

Algorithm
121×rewrite-expression-head
Calls

386 calls:

1.4s
(/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0))
1.4s
(/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0))
1.1s
(* (/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) 2.0) (sin y))
1.1s
(* (/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0)) (sin y))
1.1s
(* (/ (+ (/ (pow x 5) 60) (+ (+ (/ (pow x 3) 3) x) x)) (sqrt 2.0)) (sin y))
Rules
7481×times-frac
6731×*-un-lft-identity
6118×add-sqr-sqrt
4170×add-cube-cbrt
1590×add-exp-log
1249×unpow-prod-down
1215×sqrt-prod
1057×add-cbrt-cube
864×distribute-lft-out
749×associate-/l*
703×add-log-exp
677×difference-of-squares
676×pow1
594×associate-*l*
519×distribute-lft-out--
495×associate-/r*
485×div-exp
464×associate-*r*
432×sqr-pow
375×cube-prod
368×prod-exp
358×div-inv
250×exp-prod
238×associate-/r/
235×unswap-sqr cbrt-prod unpow2
232×cbrt-undiv
230×log-prod
221×associate-*l/
209×flip-- flip3--
196×log-pow
194×distribute-rgt-neg-in
192×cbrt-unprod
161×flip-+ flip3-+
151×distribute-lft-neg-in
145×pow-unpow
143×swap-sqr
135×sqrt-pow1
130×pow-exp
125×pow-to-exp
115×diff-log
110×sub-neg
108×frac-add
90×clear-num frac-2neg
84×associate-/l/
83×cbrt-div
76×pow-prod-down
69×1-exp
68×sqrt-div
66×frac-times
65×pow1/2
64×rec-exp
61×associate-*r/
59×*-commutative
56×exp-sum
49×sum-log
48×unpow3 cube-mult
44×log-div
43×pow1/3
36×tan-quot
35×rem-sqrt-square
34×frac-sub
32×neg-mul-1
31×distribute-rgt-in difference-cubes distribute-lft-in
29×pow-prod-up
26×div-sub exp-to-pow
25×associate--l+
24×pow-pow complex-mul-def +-commutative
21×pow-sqr
19×rem-log-exp
18×neg-sub0 associate--r+
16×associate-+l+
13×exp-diff pow-flip associate--l-
12×associate-+l-
11×inv-pow un-div-inv
10×neg-log
cube-div exp-lft-cube
rem-cube-cbrt cos-mult
pow2 pow-plus sin-mult
rem-exp-log *.c-commutative
difference-of-sqr-1
sqrt-unprod +.c-commutative complex-add-def
rem-square-sqrt associate--r- rem-cbrt-cube
cos-sum associate-+l+.c exp-neg pow-sub distribute-frac-neg associate-*l*.c distribute-rgt-neg-out frac-2neg.c pow-neg sin-sum tan-sum
sub0-neg sin-cos-mult associate-+r+ diff-atan sub-div diff-cos sqrt-undiv distribute-rgt-out diff-sin

regimes3.0s (0.8%)

Accuracy

Total 32.8b remaining (13.4%)

Threshold costs 7.5b (3%)

5.1b-1224.4%2isqrt (example 3.6)
4.7b82.5%quadm (p42, negative)
4.6b83.8%quadp (p42, positive)
4.5b84.4%quad2p (problem 3.2.1, positive)
3.4b0%expq3 (problem 3.4.2)

localize2.5s (0.6%)

bsearch1.4s (0.3%)

end0.0ms (0.0%)