Details

simplify5.1m (44.0%)

sample4.5m (38.4%)

Algorithm
56×intervals
16×halfpoints
Results
48.4s66710×body1280valid
34.7s17577×body2560valid
20.2s42801×body640valid
11.8s12718×body10240exit
8.2s94377×body80valid
5.8s20173×body320valid
4.8s62982×body80nan
2.1s10324×body160valid
1.6s47457×pre80true
536.0ms652×body1280nan
370.0ms452×body5120valid
368.0ms667×body640nan
111.0ms349×body320nan
33.0ms179×body160nan

series50.0s (7.1%)

Calls

401 calls:

830.0ms
(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
728.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
720.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
719.0ms
(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
633.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

prune43.5s (6.2%)

rewrite19.8s (2.8%)

Algorithm
122×rewrite-expression-head
Calls

401 calls:

606.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))
552.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
436.0ms
(- (sin (+ x eps)) (sin x))
436.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
291.0ms
(* (- (exp (* a eps)) 1.0) (+ (* (* b b) (+ (* (* 1/6 (pow eps 3)) b) (* 1/2 (* eps eps)))) (* eps b)))
Rules
3762×*-un-lft-identity
3643×add-sqr-sqrt
2906×times-frac
2156×add-cube-cbrt
1257×add-exp-log
1031×add-cbrt-cube
747×sqrt-prod
742×pow1
685×add-log-exp
628×difference-of-squares
471×associate-*l*
458×distribute-lft-out--
386×associate-/l*
383×distribute-lft-out
382×associate-/r*
371×associate-*r*
351×cbrt-prod
304×prod-exp
295×unpow-prod-down
245×pow-unpow
242×div-exp
226×log-prod
221×flip3-- flip--
213×log-pow
210×cbrt-unprod
192×cbrt-undiv
189×exp-prod
174×associate-/r/
171×flip-+ flip3-+
161×div-inv
150×unswap-sqr
149×sqr-pow
128×associate-*l/
110×sqrt-div
109×sub-neg
106×diff-log
104×pow-prod-down
97×distribute-rgt-neg-in
91×cube-prod
87×associate-*r/
79×sqrt-pow1
76×frac-2neg clear-num
73×*-commutative
72×cbrt-div
63×associate-/l/
59×pow1/3
58×pow1/2 frac-times
49×exp-sum
48×swap-sqr
47×sum-log
40×pow-to-exp pow-exp
38×distribute-rgt-in rem-sqrt-square log-div distribute-lft-in
32×tan-quot div-sub
30×distribute-lft-neg-in frac-add neg-mul-1
27×unpow2 frac-sub
26×+-commutative
25×associate--l+
21×1-exp rec-exp rem-log-exp
19×pow-prod-up associate--r+
18×pow-pow
17×unpow3 cube-mult
15×exp-diff neg-sub0
13×pow-sqr complex-mul-def pow-flip
11×associate-+l+
10×associate--l-
8×rem-exp-log neg-log
6×rem-cube-cbrt inv-pow distribute-frac-neg associate-+l-
5×pow-plus pow2
4×cube-div sqrt-unprod associate-+r+ rem-cbrt-cube *.c-commutative exp-to-pow
3×difference-cubes pow3 +.c-commutative
2×cos-sum exp-neg complex-add-def sin-mult tan-sum frac-2neg.c sin-sum
1×sub0-neg un-div-inv associate-+l+.c distribute-lft-neg-out diff-atan sin-cos-mult diff-cos rem-square-sqrt associate-*l*.c quot-tan cos-mult diff-sin

regimes4.0s (0.6%)

Accuracy

Total 20.6b remaining (13%)

Threshold costs 6.8b (4.3%)

4.7b82.8%quadp (p42, positive)
3.5b59.5%expq3 (problem 3.4.2)
2.1b77.3%2nthrt (problem 3.4.6)
1.3b94.8%quad2m (problem 3.2.1, negative)
1.2b94.9%quadm (p42, negative)

localize3.4s (0.5%)

bsearch2.3s (0.3%)

end1.0ms (0.0%)