Details

sample4.5m (40.9%)

Algorithm
56×intervals
16×halfpoints
Results
50.5s67398×body1280valid
34.2s16865×body2560valid
19.2s42563×body640valid
11.6s13183×body10240exit
9.1s93544×body80valid
6.4s20713×body320valid
4.5s63024×body80nan
2.0s10683×body160valid
1.8s47478×pre80true
807.0ms442×body5120valid
514.0ms643×body1280nan
511.0ms304×body320nan
468.0ms643×body640nan
36.0ms190×body160nan

simplify4.1m (37.3%)

series59.7s (9.0%)

Calls

374 calls:

1.8s
(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.6s
(cbrt (cbrt (fma x 0.3333333333333333 (* 0.0021164021164021165 (pow x 5)))))
1.6s
(* (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))) (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
1.5s
(cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x)))
1.4s
(cbrt (cbrt (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))

prune58.8s (8.8%)

rewrite15.5s (2.3%)

Algorithm
122×rewrite-expression-head
Calls

374 calls:

454.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
396.0ms
(- (/ 1.0 x) (/ 1.0 (tan x)))
312.0ms
(* x (+ (* (* 1/2 (* a a)) x) a))
289.0ms
(/ (/ (+ 0 (* c a)) (+ (- (sqrt (fma (- c) a (* b_2 b_2))) b_2) (+ b_2 (- b_2)))) a)
279.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
Rules
8290×*-un-lft-identity
7452×add-sqr-sqrt
6845×times-frac
5772×add-cube-cbrt
3750×prod-diff
2662×sqrt-prod
1118×add-exp-log
901×unpow-prod-down add-cbrt-cube
869×pow1
734×associate-*l*
725×distribute-lft-out
674×difference-of-squares
626×distribute-lft-out--
605×add-log-exp
494×log-prod
433×associate-/l* fma-neg
395×associate-/r/
394×associate-*r*
386×div-inv
364×expm1-log1p-u
363×log1p-expm1-u
358×cbrt-prod
325×sqr-pow
283×associate-/r*
265×cube-prod
262×associate-+l+ prod-exp
223×log-pow div-exp
221×flip-- flip3--
210×distribute-rgt-neg-in
198×exp-sum
194×unswap-sqr
176×flip-+ flip3-+
171×cbrt-unprod
161×cbrt-undiv
159×distribute-lft-neg-in
129×pow-prod-down sqrt-pow1
109×exp-prod
104×associate-*l/
101×tan-quot
100×sub-neg
95×diff-log sqrt-div
90×pow-unpow pow1/2
87×fma-def
82×unpow2
77×associate-*r/
68×associate-+r+
65×associate-/l/ frac-2neg clear-num
63×unpow3 cube-mult
62×frac-times
60×*-commutative
54×pow-prod-up
53×neg-mul-1
52×pow-to-exp pow-exp
47×pow1/3
45×distribute-rgt-in distribute-lft-in
41×log-div swap-sqr
38×div-sub
33×fma-udef
29×rem-sqrt-square
28×frac-add
27×sum-log rem-log-exp
26×pow-sqr
20×pow-flip 1-exp
17×+-commutative rec-exp
16×associate--r+
15×associate--l+
13×pow-pow complex-mul-def neg-sub0
10×pow-div exp-diff associate-+l-
9×pow-plus frac-sub
8×cbrt-div
7×associate--l- sqrt-unprod pow2
6×inv-pow neg-log exp-to-pow
4×rem-exp-log distribute-frac-neg *.c-commutative
3×rem-cube-cbrt +.c-commutative distribute-rgt-out-- sin-sum
2×sin-cos-mult difference-cubes associate-+r- exp-neg complex-add-def rem-square-sqrt cos-sum sin-mult tan-sum
1×associate-+l+.c un-div-inv log1p-udef associate--r- diff-atan log1p-expm1 sub-div diff-cos expm1-log1p associate-*l*.c rem-cbrt-cube expm1-udef sqrt-undiv diff-sin

regimes4.5s (0.7%)

Accuracy

Total 28.1b remaining (15.5%)

Threshold costs 6.5b (3.6%)

5.7b33.2%expq3 (problem 3.4.2)
4.2b85.2%quad2p (problem 3.2.1, positive)
4.1b85%quadm (p42, negative)
3.5b88%quadp (p42, positive)
2.3b90.8%quad2m (problem 3.2.1, negative)

localize3.5s (0.5%)

bsearch3.3s (0.5%)

end1.0ms (0.0%)