Details

simplify5.7m (45.0%)

sample4.5m (35.8%)

Algorithm
56×intervals
16×halfpoints
Results
50.5s66710×body1280valid
34.3s17577×body2560valid
20.3s42801×body640valid
11.1s12718×body10240exit
8.1s94377×body80valid
7.5s20173×body320valid
5.1s62982×body80nan
2.5s10324×body160valid
1.6s47457×pre80true
546.0ms652×body1280nan
457.0ms452×body5120valid
441.0ms667×body640nan
111.0ms349×body320nan
32.0ms179×body160nan

prune1.1m (8.8%)

series49.2s (6.5%)

Calls

380 calls:

942.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
926.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (cbrt (pow (* (tan x) (tan eps)) (* 2 3))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
921.0ms
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
616.0ms
(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
589.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite19.9s (2.6%)

Algorithm
122×rewrite-expression-head
Calls

380 calls:

882.0ms
(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
478.0ms
(* (sqrt (* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
475.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
396.0ms
(* (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))) (/ (sqrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))
262.0ms
(/ (+ 1.0 (/ (- (/ 0.3333333333333333 N) 0.5) N)) N)
Rules
12036×*-un-lft-identity
11136×times-frac
10176×add-sqr-sqrt
8567×sqrt-prod
8453×add-cube-cbrt
5614×prod-diff
1468×distribute-lft-out
1246×add-exp-log
958×add-cbrt-cube
841×distribute-rgt-in distribute-lft-in
810×pow1
783×unpow-prod-down
632×difference-of-squares
622×div-inv
607×add-log-exp
567×associate-*l*
543×associate-/l*
482×associate-/r/
471×fma-neg
421×distribute-lft-out--
410×associate-*r*
369×expm1-log1p-u
367×log1p-expm1-u
364×distribute-rgt-neg-in
363×cbrt-prod
348×associate-/r*
333×distribute-lft-neg-in
330×log-prod
320×prod-exp
291×sqrt-div
289×sqr-pow
283×pow-unpow
260×div-exp
256×flip-+ flip3-+
248×associate-+l+
226×swap-sqr
221×cube-prod
209×log-pow
201×flip-- flip3--
195×cbrt-unprod
183×exp-prod
176×exp-sum
172×cbrt-undiv
158×unswap-sqr
130×pow-prod-down
121×associate-*l/
116×sqrt-pow1
111×neg-mul-1
109×sub-neg
100×diff-log
95×associate-*r/
83×pow1/2
77×frac-times
74×frac-2neg clear-num
71×tan-quot
69×pow-exp
68×associate-/l/ pow-to-exp
67×fma-def
65×*-commutative
59×unpow3 cube-mult
56×pow-prod-up
37×pow1/3
36×unpow2
35×log-div
34×rem-sqrt-square div-sub
32×cbrt-div
29×fma-udef
26×pow-sqr
24×1-exp rec-exp
21×frac-sub rem-log-exp
18×sum-log
16×pow-pow
15×exp-diff frac-add pow-plus
14×associate--l+
13×complex-mul-def
12×+-commutative neg-sub0
8×rem-exp-log pow2
7×associate--l- associate--r+ pow-flip sin-mult
6×sqrt-unprod sqrt-undiv neg-log associate-+l-
5×cos-mult
4×cube-div un-div-inv inv-pow *.c-commutative distribute-frac-neg exp-to-pow
3×rem-cube-cbrt +.c-commutative rem-square-sqrt hypot-def cos-sum
2×sin-cos-mult rem-cbrt-cube difference-cubes log1p-udef frac-2neg.c exp-neg log1p-expm1 sub-div complex-add-def tan-sum sin-sum
1×sub0-neg associate-+r- diff-atan diff-cos expm1-log1p associate-*l*.c distribute-rgt-neg-out expm1-udef associate-+l+.c diff-sin

regimes4.1s (0.5%)

Accuracy

Total 23.6b remaining (12.5%)

Threshold costs 8.7b (4.6%)

4.5b84.3%quadp (p42, positive)
3.7b86.5%quadm (p42, negative)
3.3b55.6%expq3 (problem 3.4.2)
2.1b77.3%2nthrt (problem 3.4.6)
1.3b94.8%quad2m (problem 3.2.1, negative)

localize3.4s (0.4%)

bsearch2.6s (0.3%)

end1.0ms (0.0%)