Details

simplify5.2m (39.0%)

sample5.1m (38.4%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66504×body1280valid
40.2s17410×body2560valid
25.8s41582×body640valid
16.0s12605×body10240exit
11.3s94265×body80valid
9.0s20853×body320valid
6.9s63734×body80nan
3.7s10869×body160valid
2.0s47349×pre80true
1.3s638×body1280nan
566.0ms492×body5120valid
564.0ms631×body640nan
238.0ms372×body320nan
66.0ms210×body160nan

prune1.9m (14.4%)

series38.9s (4.9%)

Calls

388 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
652.0ms
(log (exp (* (cbrt (- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))) (cbrt (- (cbrt (* (* (pow (+ x 1) (/ 1 n)) (pow (+ x 1) (/ 1 n))) (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))))))
512.0ms
(cbrt (* (cbrt x) (cbrt x)))
485.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite14.9s (1.9%)

Algorithm
120×rewrite-expression-head
Calls

388 calls:

1.0s
(* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27))
660.0ms
(/ (* x (+ (* 1/91125 (* (* (* x x) (* x x)) (* x x))) 1/27)) (+ (* 1/3 1/3) (- (* (* (* x x) 1/45) (* (* x x) 1/45)) (* 1/3 (* (* x x) 1/45)))))
370.0ms
(- (- (* -2/3 (* (* eps eps) eps)) (* 2 eps)) (* 2/5 (pow eps 5)))
341.0ms
(* (* (* (* a x) (* a x)) (* a x)) 1/6)
315.0ms
(* (cbrt (+ -1 (- (* (* x x) -1/2) x))) (cbrt (+ -1 (- (* (* x x) -1/2) x))))
Rules
4622×*-un-lft-identity
3611×add-sqr-sqrt
3437×times-frac
2332×pow1
2190×add-cube-cbrt
1419×add-exp-log
1376×sqrt-prod
1263×add-cbrt-cube
921×distribute-lft-out
702×add-log-exp
630×pow-prod-down
565×pow-prod-up
518×associate-*r*
486×associate-*l*
470×difference-of-squares
465×prod-exp
420×cbrt-unprod
376×insert-posit16
365×distribute-lft-out--
333×div-inv
305×associate-/r*
298×associate-/l*
277×log-prod
270×pow-sqr
229×flip3-- flip--
222×associate-/r/ div-exp
213×flip-+ flip3-+
204×pow-plus swap-sqr cbrt-prod
191×unswap-sqr
181×associate-*l/
173×associate-*r/
156×cbrt-undiv
144×pow2
143×sqrt-div
138×exp-prod
135×frac-times
115×diff-log
109×sub-neg
104×pow-unpow
94×*-commutative
92×pow-flip
91×frac-sub
90×sqrt-pow1
79×tan-quot associate-+r+
78×cbrt-div
74×associate-/l/
72×pow1/2
65×frac-2neg clear-num
58×sum-log
56×unpow-prod-down
49×log-pow
48×pow1/3
44×1-exp rec-exp
43×inv-pow
39×associate-+l+ difference-of-sqr-1
37×+-commutative
31×distribute-rgt-in distribute-lft-in
29×associate--l+ rem-sqrt-square
28×frac-add
27×distribute-rgt-neg-in
26×sqr-pow
24×un-div-inv
22×log-div
19×div-sub
16×rem-log-exp
15×associate--l-
13×pow-pow complex-mul-def
12×pow-exp
11×pow-to-exp
10×associate--r+ distribute-rgt1-in
9×sin-mult distribute-rgt-out
8×neg-sub0 neg-log
7×associate-+l-
5×cos-mult sin-sum sub-div distribute-rgt-out--
4×associate-+r- cube-unmult rem-exp-log
3×exp-sum *.c-commutative sqrt-unprod sqr-sin +.c-commutative cos-sum
2×associate-*l*.c sin-cos-mult distribute-lft1-in tan-sum frac-2neg-c exp-to-pow complex-add-def rem-square-sqrt
1×exp-diff diff-atan pow3 log-rec +-inverses diff-sin associate-+l+.c rem-cbrt-cube diff-cos

localize5.3s (0.7%)

regimes4.7s (0.6%)

Accuracy

Total 26.3b remaining (20.5%)

Threshold costs 5.4b (4.2%)

4.9b82.3%quadm (p42, negative)
4.8b82.6%quad2p (problem 3.2.1, positive)
4.7b82.8%quadp (p42, positive)
3.4b0%expq3 (problem 3.4.2)
1.6b81.6%2nthrt (problem 3.4.6)

bsearch1.4s (0.2%)

end1.0ms (0.0%)