Details

simplify5.2m (42.5%)

sample4.6m (37.7%)

Algorithm
56×intervals
16×halfpoints
Results
52.2s66935×body1280valid
33.8s17227×body2560valid
19.4s42341×body640valid
10.8s13053×body10240exit
8.6s93690×body80valid
6.6s20770×body320valid
5.7s63040×body80nan
1.9s10808×body160valid
1.7s47470×pre80true
625.0ms711×body1280nan
425.0ms641×body640nan
353.0ms492×body5120valid
116.0ms350×body320nan
34.0ms179×body160nan

prune57.0s (7.8%)

series53.2s (7.3%)

Calls

399 calls:

1.4s
(/ (+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
765.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
684.0ms
(+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))
647.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
524.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))

rewrite24.6s (3.4%)

Algorithm
122×rewrite-expression-head
Calls

399 calls:

819.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
681.0ms
(- (+ (/ 0.3333333333333333 (pow N 3)) (/ 1.0 N)) (/ (/ 0.5 N) N))
632.0ms
(/ (+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
476.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
405.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))
Rules
4790×*-un-lft-identity
4718×add-sqr-sqrt
4173×times-frac
2667×add-cube-cbrt
2149×associate-*l/
1972×cbrt-div
1634×add-exp-log
1140×add-cbrt-cube
1038×cbrt-prod
915×associate-*r/
887×flip-+ flip3-+
882×frac-times
869×difference-of-squares
698×pow1
697×unpow-prod-down
668×add-log-exp
640×associate-*r*
611×sqrt-prod
576×associate-*l*
564×distribute-lft-out
560×frac-add
541×distribute-lft-out--
502×associate-/l*
451×prod-exp
448×div-exp
439×frac-sub
434×flip3-- flip--
407×associate-/r*
342×associate-/l/
311×sqr-pow
290×div-inv
281×cube-prod
250×cbrt-unprod
239×cbrt-undiv
237×associate-/r/
212×unswap-sqr
211×pow-unpow
161×swap-sqr
144×log-prod
115×distribute-rgt-neg-in
111×pow-prod-down
97×diff-log
95×unpow2
92×sub-neg
86×clear-num frac-2neg
82×pow1/3
79×1-exp
78×log-pow
70×sqrt-div
69×*-commutative
59×pow-exp
57×pow-to-exp
53×distribute-lft-neg-in neg-mul-1
51×sum-log
50×exp-sum
47×exp-prod
42×distribute-rgt-in distribute-lft-in
39×log-div rec-exp
35×div-sub
30×+-commutative tan-quot
27×unpow3 cube-mult
26×pow1/2 rem-sqrt-square sqrt-pow1
21×neg-sub0
20×associate--l+
19×associate-+l+ pow-pow
17×pow-prod-up rem-log-exp
15×associate--l- associate--r+
13×pow-sqr complex-mul-def
12×neg-log
11×associate-+l-
10×cube-div difference-cubes
9×exp-diff rem-cube-cbrt
8×exp-neg distribute-rgt-out--
7×pow2 pow-flip pow-plus
5×un-div-inv inv-pow rem-cbrt-cube
4×rem-exp-log *.c-commutative associate-+r+ distribute-frac-neg sin-mult
3×sub-div +.c-commutative
2×cos-sum sin-sum associate--r- complex-add-def tan-sum frac-2neg.c
1×sub0-neg sin-cos-mult pow3 associate-+l+.c diff-atan diff-cos associate-+r- cos-mult associate-*l*.c exp-to-pow diff-sin

regimes3.9s (0.5%)

Accuracy

Total 18.9b remaining (15.3%)

Threshold costs 7.1b (5.7%)

3.9b85.1%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)
1.3b85.3%2nthrt (problem 3.4.6)
1.2b94.9%quad2p (problem 3.2.1, positive)
1.2b95.1%quadp (p42, positive)

localize3.5s (0.5%)

bsearch2.4s (0.3%)

end2.0ms (0.0%)